JEE Main & Advanced Mathematics Probability Question Bank

done Conditional probability bayes theorem Total Questions - 35

• question_answer1)
  Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is 11, if 5 appears on the first
  A)
                  \[\frac{1}{36}\]     done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  \[\frac{5}{6}\]        done clear
  D)
                  None of these done clear
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• question_answer2)
  If \[P\,(A)=\frac{1}{2},\,\,P\,(B)=\frac{1}{3}\] and \[P\,(A\cap B)=\frac{1}{4},\] then \[P\,\left( \frac{B}{A} \right)=\]
  A)
                  1              done clear
  B)
                  0              done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
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• question_answer3)
  If A and B are two events such that \[P\,(A)\ne 0\] and \[P\,(B)\ne 1,\] then \[P\,\left( \frac{{\bar{A}}}{{\bar{B}}} \right)=\] [IIT 1982; RPET 1995, 2000; DCE 2000; UPSEAT 2001]
  A)
                  \[1-P\,\left( \frac{A}{B} \right)\]            done clear
  B)
                  \[1-P\,\left( \frac{{\bar{A}}}{B} \right)\] done clear
  C)
                  \[\frac{1-P\,(A\cup B)}{P\,(\bar{B})}\]                done clear
  D)
                  \[\frac{P\,(\bar{A})}{P\,(\bar{B})}\] done clear
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• question_answer4)
  In a single throw of two dice what is the probability of obtaining a number greater than 7,  if 4 appears on the first dice
  A)
                  \[\frac{1}{3}\]        done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{12}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer5)
  If A and B are two events such that \[P\,(A)=\frac{1}{3}\], \[P\,(B)=\frac{1}{4}\]  and \[P\,(A\cap B)=\frac{1}{5},\] then \[P\,\left( \frac{{\bar{B}}}{{\bar{A}}} \right)=\]
  A)
                  \[\frac{37}{40}\]   done clear
  B)
                  \[\frac{37}{45}\] done clear
  C)
                  \[\frac{23}{40}\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer6)
  If A and B are two events such that \[P\,(A)=\frac{3}{8},\,\] \[P\,(B)=\frac{5}{8}\] and \[P\,(A\cup B)=\frac{3}{4},\] then\[P\,\left( \frac{A}{B} \right)=\]
  A)
                  \[\frac{2}{5}\] done clear
  B)
                  \[\frac{2}{3}\] done clear
  C)
                  \[\frac{3}{5}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer7)
  If the events A and B are mutually exclusive, then \[P\left( \frac{A}{B} \right)=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[\frac{P\,(A\cap B)}{P\,(A)}\]              done clear
  D)
                  \[\frac{P\,(A\cap B)}{P\,(B)}\] done clear
  View Solution play_arrow

• question_answer8)
  If A and B are two events such that \[A\subseteq B,\] then \[P\,\left( \frac{B}{A} \right)=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  1/2          done clear
  D)
                  1/3 done clear
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• question_answer9)
  If A and B are two independent events, then \[P\,\left( \frac{A}{B} \right)=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[P\,(A)\]  done clear
  D)
                  \[P\,(B)\] done clear
  View Solution play_arrow

• question_answer10)
  If E and F are independent events such that \[0<P(E)<1\] and \[0<P\,(F)<1,\] then                              [IIT 1989]
  A)
                  E and \[{{F}^{c}}\](the complement of the event F) are independent done clear
  B)
                  \[{{E}^{c}}\]and \[{{F}^{c}}\]are independent done clear
  C)
                  \[P\,\left( \frac{E}{F} \right)+P\,\left( \frac{{{E}^{c}}}{{{F}^{c}}} \right)=1\] done clear
  D)
                  All of the above done clear
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• question_answer11)
  If \[4\,P(A)=6\,P\,(B)=10\,P\,(A\cap B)=1,\] then \[P\,\left( \frac{B}{A} \right)=\] [MP PET 2003]
  A)
                  \[\frac{2}{5}\]        done clear
  B)
                  \[\frac{3}{5}\] done clear
  C)
                  \[\frac{7}{10}\]     done clear
  D)
                  \[\frac{19}{60}\] done clear
  View Solution play_arrow

• question_answer12)
  For a biased die, the probabilities for different faces to turn up are

  Face :	1	2	3	4	5	6
  Probability :	0.2	0.22	0.11	0.25	0.05	0.17

  The die is tossed and you are told that either face 4 or face 5 has turned up. The probability that it is face 4 is
  A)
                  \[\frac{1}{6}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{5}{6}\]        done clear
  D)
                  None of these done clear
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• question_answer13)
  A pair has two children. If one of them is boy, then the probability that other is also a boy, is
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer14)
  Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail, is
  A)
                  \[\frac{1}{7}\]        done clear
  B)
                  \[\frac{1}{8}\] done clear
  C)
                  \[\frac{2}{7}\]        done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer15)
  If A and B are two independent events such that \[P\,(A)=\frac{1}{2},\,\,P(B)=\frac{1}{5},\] then
  A)
                  \[P\,\left( \frac{A}{B} \right)=\frac{1}{2}\]        done clear
  B)
                  \[P\,\left( \frac{A}{A\cup B} \right)=\frac{5}{6}\] done clear
  C)
                  \[P\,\left( \frac{A\cap B}{{A}'\cup {B}'} \right)=0\]           done clear
  D)
                  All of the above done clear
  View Solution play_arrow

• question_answer16)
  For two events A and B, if \[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\] and \[P\,\left( \frac{B}{A} \right)=\frac{1}{2},\] then
  A)
                  A and B are independent     done clear
  B)
                  \[P\,\left( \frac{{{A}'}}{B} \right)=\frac{3}{4}\] done clear
  C)
                  \[P\,\left( \frac{{{B}'}}{{{A}'}} \right)=\frac{1}{2}\]       done clear
  D)
                  All of the above done clear
  View Solution play_arrow

• question_answer17)
  A biased die is tossed and the respective probabilities for various faces to turn up are given below

  Face :	1	2	3	4	5	6
  Probability :	0.1	0.24	0.19	0.18	0.15	0.14

  If an even face has turned up, then the probability that it is face 2 or face 4, is [MNR 1992]
  A)
                  0.25        done clear
  B)
                  0.42 done clear
  C)
                  0.75        done clear
  D)
                  0.9 done clear
  View Solution play_arrow

• question_answer18)
  If two events A and B are such that \[P({{A}^{c}})=0.3,\,P(B)=0.4\] and \[P(A{{B}^{c}})=0.5,\] then \[P[B/(A\cup {{B}^{c}})]\] is equal to [IIT 1994]
  A)
                  \[\frac{1}{2}\]        done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer19)
  A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are legible. The probability that it came from LONDON is
  A)
                  \[\frac{5}{17}\]     done clear
  B)
                  \[\frac{12}{17}\] done clear
  C)
                  \[\frac{17}{30}\]   done clear
  D)
                  \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer20)
  Let \[0<P(A)<1\], \[0<P(B)<1\] and \[P(A\cup B)=\] \[P(A)+P(B)-P(A)\,P(B).\] Then                               [IIT 1995]
  A)
                  \[P(B/A)=P(B)-P(A)\] done clear
  B)
                  \[P({{A}^{c}}\cup {{B}^{c}})=P({{A}^{c}})+P({{B}^{c}})\] done clear
  C)
                  \[P{{(A\cup B)}^{c}}=P({{A}^{c}})\,P({{B}^{c}})\] done clear
  D)
                  \[P(A/B)=P(A)\] done clear
  View Solution play_arrow

• question_answer21)
  For a biased die the probabilities for different faces to turn up are given below

  Face :	1	2	3	4	5	6
  Probability :	0.1	0.32	0.21	0.15	0.05	0.17

  The die is tossed and you are told that either face 1 or 2 has  turned up. Then the probability that it is face 1, is    [IIT 1981]
  A)
                  \[\frac{5}{21}\]     done clear
  B)
                  \[\frac{5}{22}\] done clear
  C)
                  \[\frac{4}{21}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer22)
  In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is [MNR 1988]
  A)
                  \[\frac{1}{5}\]        done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{1}{3}\]        done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer23)
  There are 3 bags which are known to contain 2 white and 3 black balls; 4 white and 1 black balls and 3 white and 7 black balls respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is
  A)
                  \[\frac{7}{15}\]     done clear
  B)
                  \[\frac{5}{19}\] done clear
  C)
                  \[\frac{3}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer24)
  In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing, is
  A)
                  \[\frac{37}{40}\]   done clear
  B)
                  \[\frac{1}{37}\] done clear
  C)
                  \[\frac{36}{37}\]   done clear
  D)
                  \[\frac{1}{9}\] done clear
  View Solution play_arrow

• question_answer25)
  A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then \[P\,\left( \frac{E}{F} \right)=\]    [MP PET 1996]
  A)
                  \[\frac{3}{4}\]        done clear
  B)
                  \[\frac{3}{8}\] done clear
  C)
                  \[\frac{1}{2}\]        done clear
  D)
                  \[\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer26)
  A and B are two events such that P = 0.8, P=0.6 and \[P(A\cap B)=0.5,\] then the value of \[P\,(A/B)\] is
  A)
                  \[\frac{5}{6}\]        done clear
  B)
                  \[\frac{5}{8}\] done clear
  C)
                  \[\frac{9}{10}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer27)
  If \[\bar{E}\] and \[\bar{F}\] are the complementary events of events E and F respectively and if \[0<P\,(F)<1,\]then           [IIT 1998]
  A)
                  \[P\,(E/F)+P\,(\bar{E}/F)=1\] done clear
  B)
                  \[P\,(E/F)+P\,(E/\bar{F})=1\] done clear
  C)
                  \[P\,(\bar{E}/F)+P\,(E/\bar{F})=1\] done clear
  D)
                  \[P\,(E/\bar{F})+P\,(\bar{E}/\bar{F})=1\]  done clear
  View Solution play_arrow

• question_answer28)
  For two events A and B, if \[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\] and \[P\left( \frac{B}{A} \right)=\frac{1}{2}\], then                                          [MP PET 2003]
  A)
                  A and B are independent     done clear
  B)
                  \[P\left( \frac{{{A}'}}{B} \right)=\frac{3}{4}\] done clear
  C)
                  \[P\left( \frac{{{B}'}}{{{A}'}} \right)=\frac{1}{2}\]         done clear
  D)
                  All of these done clear
  View Solution play_arrow

• question_answer29)
  Two cards are drawn one by one from a pack of cards.  The probability of getting first card an ace and second a colored one is (before drawing second card first card is not placed again in the pack)                                       [UPSEAT 1999; 2003]
  A)
                  \[\frac{1}{26}\]     done clear
  B)
                  \[\frac{5}{52}\] done clear
  C)
                  \[\frac{5}{221}\]   done clear
  D)
                  \[\frac{4}{13}\] done clear
  View Solution play_arrow

• question_answer30)
  One dice is thrown three times and the sum of the thrown numbers is 15. The probability for which number 4 appears in first throw                                            [MP PET 2004]
  A)
                  \[\frac{1}{18}\]     done clear
  B)
                  \[\frac{1}{36}\] done clear
  C)
                  \[\frac{1}{9}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer31)
  One ticket is selected at random from 100 tickets numbered 00, 01, 02, ...... 98, 99. If X and Y denote the sum and the product of the digits on the tickets, then \[P\,(X=9/Y=0)\] equals
  A)
                  \[\frac{1}{19}\]     done clear
  B)
                  \[\frac{2}{19}\] done clear
  C)
                  \[\frac{3}{19}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer32)
  A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six, is
  A)
                  \[\frac{3}{8}\]        done clear
  B)
                  \[\frac{1}{5}\] done clear
  C)
                  \[\frac{3}{4}\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer33)
  A bag ?A? contains 2 white and 3 red balls and bag ?B? contains 4 white and 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag ?B? was [BIT Ranchi 1988; IIT 1976]
  A)
                  \[\frac{5}{14}\]     done clear
  B)
                  \[\frac{5}{16}\] done clear
  C)
                  \[\frac{5}{18}\]     done clear
  D)
                  \[\frac{25}{52}\]   done clear
  View Solution play_arrow

• question_answer34)
  A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls.  One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is                                            [EAMCET 2003]
  A)
                  \[\frac{2}{15}\]     done clear
  B)
                  \[\frac{7}{15}\] done clear
  C)
                  \[\frac{8}{15}\]     done clear
  D)
                  \[\frac{14}{15}\] done clear
  View Solution play_arrow

• question_answer35)
  Bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted it is green. The probability that it comes bag B       [DCE 2005]
  A)
                  \[\frac{2}{7}\]        done clear
  B)
                  \[\frac{2}{3}\] done clear
  C)
                  \[\frac{3}{7}\]        done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow