JEE Main & Advanced Mathematics Probability Question Bank

done Odds in favour and odds against Addition theorem on probability Total Questions - 70

• question_answer1)
  If the odds against an event be 2 : 3, then the probability of its occurrence is
  A)
                                                                                              \[\frac{1}{5}\]                                                                                            done clear
  B)
                                                                                              \[\frac{2}{5}\] done clear
  C)
                                                                                              \[\frac{3}{5}\]                                                                                            done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer2)
  If the odds in favour of an event be 3 : 5, then the probability of non-occurrence of the event is
  A)
                                                                                              \[\frac{3}{5}\]                                                                                            done clear
  B)
                                                                                              \[\frac{5}{3}\] done clear
  C)
                                                                                              \[\frac{3}{8}\]                                                                                            done clear
  D)
                                                                                              \[\frac{5}{8}\] done clear
  View Solution play_arrow

• question_answer3)
  A card is drawn from a pack of 52 cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet
  A)
                  17 : 52    done clear
  B)
                  52 : 17 done clear
  C)
                  9 : 4        done clear
  D)
                  4 : 9 done clear
  View Solution play_arrow

• question_answer4)
  An event has odds in favour 4 : 5, then the probability that event occurs, is
  A)
                                                                                              \[\frac{1}{5}\]                                                                                            done clear
  B)
                                                                                              \[\frac{4}{5}\] done clear
  C)
                                                                                              \[\frac{4}{9}\]                                                                                            done clear
  D)
                                                                                              \[\frac{5}{9}\] done clear
  View Solution play_arrow

• question_answer5)
  For an event, odds against is 6 : 5. The probability that event does not occur, is
  A)
                                                                                              \[\frac{5}{6}\]                                                                                            done clear
  B)
                                                                                             \[\frac{6}{11}\] done clear
  C)
                                                                                             \[\frac{5}{11}\]                                                                                           done clear
  D)
                                                                                              \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer6)
  In a horse race the odds in favour of three horses are \[1:2\], \[1:3\] and \[1:4\]. The probability that one of the horse will win the race is
  A)
                                                                                            \[\frac{37}{60}\]                                                                                         done clear
  B)
                                                                                            \[\frac{47}{60}\] done clear
  C)
                                                                                              \[\frac{1}{4}\]                                                                                            done clear
  D)
                                                                                              \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer7)
  The odds against a certain event is 5 : 2 and the odds in favour of another event is  6 : 5. If both the events are independent, then the probability that at least one of the events will happen is                                  [RPET 1997]
  A)
                                                                                            \[\frac{50}{77}\]                                                                                         done clear
  B)
                                                                                            \[\frac{52}{77}\] done clear
  C)
                                                                                            \[\frac{25}{88}\]                                                                                         done clear
  D)
                                                                                            \[\frac{63}{88}\] done clear
  View Solution play_arrow

• question_answer8)
  If odds against solving a question by three students are 2 : 1, \[5:2\] and \[5:3\] respectively, then probability that the question is solved only by one student is   [RPET 1999]
  A)
                                                                                            \[\frac{31}{56}\]                                                                                         done clear
  B)
                                                                                            \[\frac{24}{56}\] done clear
  C)
                                                                                            \[\frac{25}{56}\]                                                                                         done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer9)
  Three ships A, B and C sail from England to India. If the ratio of their arriving safely are 2 : 5, 3 : 7 and 6 : 11 respectively then the probability of all the ships for arriving safely is [Pb. CET 2000]
  A)
                                                                   \[\frac{18}{595}\]                                                                                       done clear
  B)
                                                                                             \[\frac{6}{17}\] done clear
  C)
                                                                                             \[\frac{3}{10}\]                                                                                           done clear
  D)
                                                                                              \[\frac{2}{7}\] done clear
  View Solution play_arrow

• question_answer10)
  A party of 23 persons take their seats at a round table. The odds against two persons sitting together are               [RPET 1999]
  A)
                  10 : 1      done clear
  B)
                  1 : 11 done clear
  C)
                  9 : 10      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer11)
  If two events A and B are such that                                                                                   \[P\,(A+B)=\frac{5}{6},\]                                                                                      \[P\,(AB)=\frac{1}{3}\,\] and                                                                                 \[P\,(\bar{A})=\frac{1}{2},\]  then the events A and B are
  A)
                  Independent done clear
  B)
                  Mutually exclusive done clear
  C)
                  Mutually exclusive and independent done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer12)
  The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is        [MNR 1987; UPSEAT 2000]
  A)
                  True        done clear
  B)
                  Wrong done clear
  C)
                  Could be either     done clear
  D)
                  Do not know done clear
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• question_answer13)
  If  A  and B are two events such that                                                                                               \[P(A)=0.4\]  ,                                                                                          \[P\,(A+B)=0.7\]  and                                                                                            \[P\,(AB)=0.2,\]  then                                                                                                \[P\,(B)=\] [MP PET 1992]
  A)
                  0.1          done clear
  B)
                  0.3 done clear
  C)
                  0.5          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer14)
  Suppose that A, B, C are events such that                                   \[P\,(A)=P\,(B)=P\,(C)=\frac{1}{4},\,P\,(AB)=P\,(CB)=0,\,P\,(AC)=\frac{1}{8},\]  then                                                                                             \[P\,(A+B)=\]                                                 [MP PET 1992]
  A)
                  0.125 done clear
  B)
                  0.25 done clear
  C)
                  0.375      done clear
  D)
                  0.5 done clear
  View Solution play_arrow

• question_answer15)
  A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is [MP PET 1989]
  A)
                                                                                             \[\frac{1}{13}\]                                                                                           done clear
  B)
                                                                                             \[\frac{1}{26}\] done clear
  C)
                                                                                              \[\frac{1}{2}\]                                                                                            done clear
  D)
                                                                                             \[\frac{7}{13}\] done clear
  View Solution play_arrow

• question_answer16)
  If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is                                                [IIT 1989]
  A)
                  0.5          done clear
  B)
                  0.44 done clear
  C)
                  0.6          done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer17)
  If                                                                  \[P\,(A)=0.4,\,\,P\,(B)=x,\,\,P\,(A\cup B)=0.7\] and the events A and B are independent,  then x =                         [CEE 1993]
  A)
                                                                                              \[\frac{1}{3}\]                                                                                            done clear
  B)
                                                                                              \[\frac{1}{2}\] done clear
  C)
                                                                                              \[\frac{2}{3}\]                                                                                            done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer18)
  If A and B are two events of a random experiment,                                                                                             \[P\,(A)=0.25\] ,                                                                                             \[P\,(B)=0.5\]  and                                                                                      \[P\,(A\cap B)=0.15,\]   then                                                                                      \[P\,(A\cap \bar{B})=\]                                                 [MP PET 1987]
  A)
                  0.1          done clear
  B)
                  0.35 done clear
  C)
                  0.15        done clear
  D)
                  0.6 done clear
  View Solution play_arrow

• question_answer19)
  If                                                                  \[P\,(A)=0.4,\,\,P\,(B)=x,\,\,P\,(A\cup B)=0.7\] and the events A and B are mutually exclusive, then                                                                                                    \[x=\]                 [MP PET 1992]
  A)
                                                                                             \[\frac{3}{10}\]                                                                                           done clear
  B)
                                                                                              \[\frac{1}{2}\] done clear
  C)
                                                                                              \[\frac{2}{5}\]                                                                                            done clear
  D)
                                                                                              \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer20)
  If A and B are any two events, then the probability that exactly one of them occur is                                   [BIT Ranchi 1990; IIT 1984; RPET 1995, 2002; MP PET 2004]
  A)
                                                                                  \[P\,(A)+P\,(B)-P\,(A\cap B)\]                                                                               done clear
  B)
                                                                                \[P\,(A)+P\,(B)-2P\,(A\cap B)\] done clear
  C)
                                                                                 \[P\,(A)+P\,(B)-P\,(A\cup B)\] done clear
  D)
                                                                                \[P\,(A)+P\,(B)-2P\,(A\cup B)\] done clear
  View Solution play_arrow

• question_answer21)
  A coin is tossed twice. If events A and B are defined as :                 A = head on first toss,                                                                                                    \[B=\] head on second toss. Then the probability of                                                                                              \[A\cup B=\]
  A)
                                                                                              \[\frac{1}{4}\]                                                                                            done clear
  B)
                                                                                              \[\frac{1}{2}\] done clear
  C)
                                                                                              \[\frac{1}{8}\]                                                                                            done clear
  D)
                                                                                              \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer22)
  If A and B are two mutually exclusive events, then                                                                                             \[P\,(A+B)=\]                          [MNR 1978; MP PET 1991, 92]
  A)
                                                                                      \[P\,(A)+P\,(B)-P\,(AB)\]                                                                                   done clear
  B)
                                                                                             \[P\,(A)-P\,(B)\] done clear
  C)
                                                                                            \[P\,(A)+P\,(B)\]                                                                                          done clear
  D)
                                                                                     \[P\,(A)+P\,(B)+P\,(AB)\] done clear
  View Solution play_arrow

• question_answer23)
  The probability of happening at least  one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then                                                                               \[P\,(\bar{A})+P\,(\bar{B})=\]                 [Roorkee 1989; IIT 1987; MP PET 1997; DCE 2001; J & K 2005]
  A)
                  0.4          done clear
  B)
                  0.8 done clear
  C)
                  1.2 done clear
  D)
                  1.4 done clear
  View Solution play_arrow

• question_answer24)
  The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in at least one subject
  A)
                  28%        done clear
  B)
                  38% done clear
  C)
                  72%        done clear
  D)
                  82% done clear
  View Solution play_arrow

• question_answer25)
  If \[P\,(A)=\frac{1}{4},\,\,P\,(B)=\frac{5}{8}\] and \[P\,(A\cup B)=\frac{3}{4},\] then \[P\,(A\cap B)=\]
  A)
                  \[\frac{1}{8}\]        done clear
  B)
                  0 done clear
  C)
                  \[\frac{3}{4}\]        done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer26)
  If A and B are two independent events such that \[P\,(A)=0.40,\,\,P\,(B)=0.50.\] Find \[P\](neither A nor B) [MP PET 1989; J & K 2005]
  A)
                  0.90        done clear
  B)
                  0.10 done clear
  C)
                  0.2          done clear
  D)
                  0.3 done clear
  View Solution play_arrow

• question_answer27)
  If A and B are two independent events, then \[P\,(A+B)=\] [MP PET 1992]
  A)
                  \[P\,(A)+P\,(B)-P\,(A)\,P\,(B)\] done clear
  B)
                  \[P\,(A)-P\,(B)\] done clear
  C)
                  \[P\,(A)+P\,(B)\] done clear
  D)
                  \[P\,(A)+P\,(B)+P\,(A)\,P\,(B)\] done clear
  View Solution play_arrow

• question_answer28)
  If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6, is
  A)
                  \[\frac{41}{100}\] done clear
  B)
                  \[\frac{33}{100}\] done clear
  C)
                  \[\frac{1}{10}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer29)
  If the probability of a horse A winning a race is 1/4 and the probability of a horse B winning the same race is 1/5, then the probability that either of them will win the race is
  A)
                  \[\frac{1}{20}\]     done clear
  B)
                  \[\frac{9}{20}\] done clear
  C)
                  \[\frac{11}{20}\]   done clear
  D)
                  \[\frac{19}{20}\] done clear
  View Solution play_arrow

• question_answer30)
  If A and B an two events such that \[P\,(A\cup B)=\frac{5}{6}\],\[P\,(A\cap B)=\frac{1}{3}\] and \[P\,(\bar{B})=\frac{1}{3},\] then \[P\,(A)=\]
  A)
                  \[\frac{1}{4}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer31)
  If A and B are two events such that \[P\,(A\cup B)\,+P\,(A\cap B)=\frac{7}{8}\] and \[P\,(A)=2\,P\,(B),\] then \[P\,(A)=\]
  A)
                  \[\frac{7}{12}\]     done clear
  B)
                  \[\frac{7}{24}\] done clear
  C)
                  \[\frac{5}{12}\]     done clear
  D)
                  \[\frac{17}{24}\] done clear
  View Solution play_arrow

• question_answer32)
  The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is [CEE 1993; Pb. CET 2004]
  A)
                  \[p+q\]   done clear
  B)
                  \[p+q-2qp\] done clear
  C)
                  \[p+q-pq\]             done clear
  D)
                  \[p+q+pq\] done clear
  View Solution play_arrow

• question_answer33)
  A and B are two independent events. The probability that both A and B occur is \[\frac{1}{6}\] and the probability that neither of them occurs is \[\frac{1}{3}\]. Then the probability of the two events are respectively                                          [Roorkee 1989]
  A)
                  \[\frac{1}{2}\]and \[\frac{1}{3}\]        done clear
  B)
                  \[\frac{1}{5}\]and \[\frac{1}{6}\] done clear
  C)
                  \[\frac{1}{2}\]and \[\frac{1}{6}\]        done clear
  D)
                  \[\frac{2}{3}\]and \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer34)
  If A and B are two independent events such that \[P\,(A\cap B')=\frac{3}{25}\] and \[P\,(A'\cap B)=\frac{8}{25},\] then \[P(A)=\] [IIT Screening]
  A)
                  \[\frac{1}{5}\]        done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{2}{5}\]        done clear
  D)
                  \[\frac{4}{5}\] done clear
  View Solution play_arrow

• question_answer35)
  Let A and B be two events such that \[P\,(A)=0.3\] and \[P\,(A\cup B)=0.8\]. If A and B are independent events, then \[P(B)=\]         [IIT 1990; UPSEAT 2001, 02]
  A)
                  \[\frac{5}{6}\]        done clear
  B)
                  \[\frac{5}{7}\] done clear
  C)
                  \[\frac{3}{5}\]        done clear
  D)
                  \[\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer36)
   For two given events A and B, \[P\,(A\cap B)=\]              [IIT 1988]
  A)
                  Not less than \[P(A)+P\,(B)-1\] done clear
  B)
                  Not greater than \[P(A)+P(B)\] done clear
  C)
                  Equal to \[P(A)+P(B)-P(A\cup B)\] done clear
  D)
                  All of the above done clear
  View Solution play_arrow

• question_answer37)
  \[P(A\cup B)=P(A\cap B)\]if and only if the relation between \[P(A)\] and \[P(B)\] is                                    [IIT 1985]
  A)
                  \[P(A)=P(\bar{A})\]              done clear
  B)
                  \[P\,(A\cap B)=P(A'\cap B')\] done clear
  C)
                  \[P\,(A)=P\,(B)\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer38)
  The two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is                           [IIT 1980; MP PET 1994]
  A)
                  0.39        done clear
  B)
                  0.25 done clear
  C)
                  0.904      done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer39)
  Twelve tickets are numbered 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{7}{12}\] done clear
  C)
                  \[\frac{5}{6}\]        done clear
  D)
                  \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer40)
  Three athlete A, B and C participate in a race competetion. The probability of winning A and B is twice of winning C. Then the probability that the race win by A or B, is
  A)
                  \[\frac{2}{3}\]        done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{4}{5}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer41)
  If \[P(A)=\frac{1}{2},\,\,P(B)=\frac{1}{3}\] and \[P(A\cap B)=\frac{7}{12},\] then the value of \[P\,({A}'\cap {B}')\] is
  A)
                  \[\frac{7}{12}\]     done clear
  B)
                  \[\frac{3}{4}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer42)
  In a city 20% persons read English newspaper, 40% read Hindi newspaper and 5% read both newspapers. The percentage of non-reader either paper is
  A)
                  60%        done clear
  B)
                  35% done clear
  C)
                  25%        done clear
  D)
                  45% done clear
  View Solution play_arrow

• question_answer43)
  The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then \[P({A}')+P({B}')=\]
  A)
                  0.9          done clear
  B)
                  1.15 done clear
  C)
                  1.1          done clear
  D)
                  1.2 done clear
  View Solution play_arrow

• question_answer44)
  The probability that a man will be alive in 20 years is \[\frac{3}{5}\] and the probability that his wife will be alive in 20 years is \[\frac{2}{3}\]. Then the probability that at least one will be alive in 20 years, is                                   [Bihar CEE 1994]
  A)
                  \[\frac{13}{15}\]   done clear
  B)
                  \[\frac{7}{15}\] done clear
  C)
                  \[\frac{4}{15}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer45)
  Given two mutually exclusive events A and B such that \[P(A)=0.45\] and \[P(B)=0.35,\] then P (A or B) = [AI CBSE 1979]
  A)
                  0.1          done clear
  B)
                  0.25 done clear
  C)
                  0.15        done clear
  D)
                  0.8 done clear
  View Solution play_arrow

• question_answer46)
  If A and B are any two events, then \[P(A\cup B)=\] [MP PET 1995]
  A)
                  \[P(A)+P(B)\] done clear
  B)
                  \[P(A)+P(B)+P(A\cap B)\] done clear
  C)
                  \[P(A)+P(B)-P(A\cap B)\] done clear
  D)
                  \[P(A)\,\,.\,\,P(B)\] done clear
  View Solution play_arrow

• question_answer47)
  If \[{{A}_{1}},\,{{A}_{2}},...{{A}_{n}}\] are any n events, then
  A)
                  \[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})=P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done clear
  B)
                  \[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})>P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done clear
  C)
                  \[P\,({{A}_{1}}\cup {{A}_{2}}\cup ...\cup {{A}_{n}})\le P\,({{A}_{1}})+P({{A}_{2}})+...+P\,({{A}_{n}})\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer48)
  In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is                                        [EAMCET 1993]
  A)
                  \[\frac{13}{25}\]   done clear
  B)
                  \[\frac{3}{25}\] done clear
  C)
                  \[\frac{17}{25}\]   done clear
  D)
                  \[\frac{8}{25}\] done clear
  View Solution play_arrow

• question_answer49)
  A, B, C are any three events. If P (S) denotes the probability of S happening  then \[P\,(A\cap (B\cup C))=\] [EAMCET 1994]
  A)
                  \[P(A)+P(B)+P(C)-P(A\cap B)-P(A\cap C)\] done clear
  B)
                  \[P(A)+P(B)+P(C)-P(B)\,P(C)\] done clear
  C)
                  \[P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer50)
  Let \[{{E}_{1}},{{E}_{2}},{{E}_{3}}\]be three arbitrary events of a sample space S.  Consider the following statements which of the following statements are correct                                          [Pb. CET 2004]
  A)
                  P (only one of them occurs)         \[=P({{\bar{E}}_{1}}{{E}_{2}}{{E}_{3}}+{{E}_{1}}{{\bar{E}}_{2}}{{E}_{3}}+{{E}_{1}}{{E}_{2}}{{\overline{E}}_{3}})\] done clear
  B)
              P (none of them occurs)                 \[=P({{\overline{E}}_{1}}+{{\overline{E}}_{2}}+{{\overline{E}}_{3}})\]           done clear
  C)
                  P (at least one of them occurs)                 \[=P({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\] done clear
  D)
                  P (all the three occurs)\[=P({{E}_{1}}+{{E}_{2}}+{{E}_{3}})\]                 where \[P({{E}_{1}})\]denotes the probability of \[{{E}_{1}}\] and \[{{\bar{E}}_{1}}\] denotes complement of \[{{E}_{1}}\]. done clear
  View Solution play_arrow

• question_answer51)
  One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is                                            [RPET 1999]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{3}{26}\] done clear
  C)
                  \[\frac{4}{13}\]     done clear
  D)
                  \[\frac{3}{13}\] done clear
  View Solution play_arrow

• question_answer52)
  The probabilities of occurrence of two events are respectively 0.21 and 0.49. The probability that both occurs simultaneously is 0.16. Then the probability that none of the two occurs is                                    [MP PET 1998]
  A)
                  0.30        done clear
  B)
                  0.46 done clear
  C)
                  0.14        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer53)
  Let A and B be events for which \[P(A)=x\], \[P(B)=y,\]\[P(A\cap B)=z,\] then \[P(\bar{A}\cap B)\] equals             [AMU 1999]
  A)
                  \[(1-x)\,y\]               done clear
  B)
                  \[1-x+\,y\] done clear
  C)
                  y ? z        done clear
  D)
    \[1-x+y-z\] done clear
  View Solution play_arrow

• question_answer54)
  The probability of solving a question by three students are \[\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}\] respectively. Probability of question is being solved will be                                          [UPSEAT 1999]
  A)
                  \[\frac{33}{48}\]   done clear
  B)
                  \[\frac{35}{48}\] done clear
  C)
                  \[\frac{31}{48}\]   done clear
  D)
                  \[\frac{37}{48}\] done clear
  View Solution play_arrow

• question_answer55)
  Let A and B are two independent events. The probability that both A and B occur together is 1/6 and the probability that neither of them occurs is 1/3. The probability of occurrence of A is                                           [RPET 2000]
  A)
                  0 or 1      done clear
  B)
                  \[\frac{1}{2}\] or \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{2}\] or \[\frac{1}{4}\]          done clear
  D)
                  \[\frac{1}{3}\] or \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer56)
  One card is drawn randomly from a pack of 52 cards, then the probability that it is a king or spade is     [RPET 2001]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{3}{26}\] done clear
  C)
                  \[\frac{4}{13}\]     done clear
  D)
                  \[\frac{3}{13}\] done clear
  View Solution play_arrow

• question_answer57)
  If \[P(A)=0.25,\,\,P(B)=0.50\] and \[P(A\cap B)=0.14,\] then \[P(A\cap \bar{B})\] is equal to                                   [RPET 2001]
  A)
                  0.61        done clear
  B)
                  0.39 done clear
  C)
                  0.48        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer58)
  If A and B are any two events, then \[P(\bar{A}\cap B)=\] [MP PET 2001]
  A)
                  \[P(\bar{A})\,\,\,P(\bar{B})\] done clear
  B)
                  \[1-P(A)-P(B)\] done clear
  C)
                  \[P(A)+P(B)-P(A\cap B)\]     done clear
  D)
                  \[P(B)-P(A\cap B)\] done clear
  View Solution play_arrow

• question_answer59)
  In two events \[P(A\cup B)=5/6\], \[P({{A}^{c}})=5/6\], \[P(B)=2/3,\] then A and B are                                         [UPSEAT 2001]
  A)
                  Independent          done clear
  B)
                  Mutually exclusive done clear
  C)
                  Mutually exhaustive              done clear
  D)
                  Dependent done clear
  View Solution play_arrow

• question_answer60)
  The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then \[P({A}')+P({B}')\] is [DCE 2002]
  A)
                  \[\frac{2}{5}\]        done clear
  B)
                  \[\frac{4}{5}\] done clear
  C)
                  \[\frac{6}{5}\]        done clear
  D)
                  \[\frac{7}{5}\] done clear
  View Solution play_arrow

• question_answer61)
  If A and B are arbitrary events, then    [DCE 2002]
  A)
                  \[P(A\cap B)\ge P(A)+P(B)\] done clear
  B)
                  \[P(A\cup B)\le P(A)+P(B)\] done clear
  C)
                  \[P(A\cap B)=P(A)+P(B)\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer62)
  If A and B are events such that \[P(A\cup B)=3/4,\] \[P(A\cap B)=1/4,\] \[P(\bar{A})=2/3,\] then \[P(\bar{A}\cap B)\] is [AIEEE 2002]
  A)
                  \[\frac{5}{12}\]     done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{5}{8}\]        done clear
  D)
                  \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer63)
  A random variable X has the probability distribution

  X	1	2	3	4	5	6	7	8
  P(X)	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

              For the events \[E=\{X\]is prime number} and \[F=\{X<4\}\], the probability of \[P(E\cup F)\] is                                           [AIEEE  2004]
  A)
                  0.50        done clear
  B)
                  0.77 done clear
  C)
                  0.35        done clear
  D)
                  0.87 done clear
  View Solution play_arrow

• question_answer64)
  If \[P(A)=P(B)=x\] and \[P(A\cap B)=P({A}'\cap {B}')=\frac{1}{3}\], then \[x=\] [UPSEAT 2003]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer65)
  If \[P(A\cup B)=0.8\] and \[P(A\cap B)=0.3,\] then \[P(\bar{A})+P(\bar{B})=\] [EAMCET 2003]
  A)
                  0.3          done clear
  B)
                  0.5 done clear
  C)
                  0.7          done clear
  D)
                  0.9 done clear
  View Solution play_arrow

• question_answer66)
  In a certain population 10% of the people are rich, 5% are famous and 3% are rich and famous. The probability that a person picked at random  from  the population is either famous or rich but not both, is equal to           [UPSEAT 2004]
  A)
                  0. 07       done clear
  B)
                  0.08        done clear
  C)
                  0. 09       done clear
  D)
                  0. 12 done clear
  View Solution play_arrow

• question_answer67)
  A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart           [RPET 2003]
  A)
                  \[\frac{4}{3}\]        done clear
  B)
                  \[\frac{16}{3}\] done clear
  C)
                  \[\frac{4}{13}\]     done clear
  D)
                  \[\frac{5}{3}\] done clear
  View Solution play_arrow

• question_answer68)
  Let A and B be two events such that \[P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}\] and \[P(\bar{A})=\frac{1}{4},\] where \[\bar{A}\] stands for complement of event A. Then events A and B are       [AIEEE 2005]
  A)
                  Independent but not equally likely done clear
  B)
                  Mutually exclusive and independent done clear
  C)
                  Equally likely and mutually exclusive done clear
  D)
                  Equally likely but not independent done clear
  View Solution play_arrow

• question_answer69)
  Let S be a set containing n elements and we select  2 subsets A and B of S at random then the probability that \[A\cup B=S\] and \[A\cap B=\varphi \] is                                       [Orissa JEE 2005]
  A)
                  \[{{2}^{n}}\]       done clear
  B)
                  \[{{n}^{2}}\] done clear
  C)
                  1/n          done clear
  D)
                  \[1/{{2}^{n}}\] done clear
  View Solution play_arrow

• question_answer70)
  Let A and B are two events and \[P({A}')=0.3\], \[P(B)=0.4,\,P(A\cap {B}')=0.5\], then \[P(A\cup {B}')\] is [Orissa JEE 2005]
  A)
                  0.5          done clear
  B)
                  0.8 done clear
  C)
                  1              done clear
  D)
                  0.1 done clear
  View Solution play_arrow