JEE Main & Advanced Mathematics Probability Question Bank

done Self Evaluation Test - Probability-II Total Questions - 70

• question_answer1)
  A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{1}{6}\] done clear
  C)
  \[\frac{1}{12}\] done clear
  D)
  \[\frac{1}{24}\] done clear
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• question_answer2)
  A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is
  A)
  \[\frac{^{20}{{C}_{10}}\times {{5}^{6}}}{{{6}^{20}}}\] done clear
  B)
  \[\frac{120\times {{5}^{7}}}{{{6}^{10}}}\] done clear
  C)
  \[\frac{84\times {{5}^{6}}}{{{6}^{10}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  Assume that each born child is equally likely to be a boy or a girl. If a family has two children, then the conditional probabilities that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl are
  A)
  \[\frac{1}{2}and\frac{1}{4}\] done clear
  B)
  \[\frac{1}{3}and\frac{1}{2}\] done clear
  C)
  \[\frac{1}{3}and\frac{1}{4}\] done clear
  D)
  \[\frac{1}{2}and\frac{1}{3}\]    done clear
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• question_answer4)
  Probability that India will win against Pakistan in a cricket match is 2/3, in series of 5 matches what is the probability that India will win the series?
  A)
  \[161/81\] done clear
  B)
  \[192/243\] done clear
  C)
  \[172/243\] done clear
  D)
  None of these done clear
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• question_answer5)
  In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is \[\frac{1}{3}.\]The probability that he copies is \[\frac{1}{6}\] and the probability that his answer is correct given that he copied it is \[\frac{1}{8}.\] The probability that he knew the answer to the question given that he correctly answered it, is
  A)
  \[\frac{24}{29}\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{3}{4}\] done clear
  D)
  \[\frac{1}{2}\]   done clear
  View Solution play_arrow

• question_answer6)
  One ticket is selected at random from 100 tickets numbered 00, 01, 02,?.98, 99, if, \[{{x}_{1}}\] and \[{{x}_{2}}\] denotes the sum and product of the digits on the tickets, then \[P({{x}_{1}}=9/{{x}_{2}}=0)\] is equal to
  A)
  2/19 done clear
  B)
  19/100 done clear
  C)
  1/50 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is
  A)
  \[\frac{1}{3}\] done clear
  B)
  \[\frac{1}{6}\] done clear
  C)
  \[\frac{1}{2}\] done clear
  D)
  \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer8)
  A die is rolled three times. Let \[{{E}_{1}}\] denote the event of getting a number larger than the previous number each time and \[{{E}_{2}}\] denote the event that the numbers (in order) form an increasing AP then
  A)
  \[P({{E}_{2}})\ge P({{E}_{1}})\] done clear
  B)
  \[P({{E}_{2}}\cap {{E}_{1}})=\frac{3}{10}\] done clear
  C)
  \[P({{E}_{2}}/{{E}_{1}})=\frac{1}{36}\] done clear
  D)
  \[P({{E}_{1}})=\frac{10}{3}P({{E}_{2}})\] done clear
  View Solution play_arrow

• question_answer9)
  A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and IV. The probabilities of the student passing in tests I, II, III are p, q and \[\frac{1}{2}\] respectively. The probability that the student is successful is \[\frac{1}{2}\] then the relation between p and q is given by
  A)
  \[pq+p=1\] done clear
  B)
  \[{{p}^{2}}+q=1\] done clear
  C)
  \[pq-1=p\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
  A)
  8/729 done clear
  B)
  8/243 done clear
  C)
  1/729 done clear
  D)
  8/9   done clear
  View Solution play_arrow

• question_answer11)
  In a class 30% students like tea, 20% like coffee and 10% like both tea and coffee. A student is selected at random then what is the probability that he does not like tea if it is known that he likes coffee?
  A)
  1/2 done clear
  B)
  3/4 done clear
  C)
  1/3 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  Abhay speaks the truth only 60%. Hasan rolls a dice blindfolded and asks abhay to tell him if the outcome is a ?Prime?. Abhay says, ?No?. What is the probability that the outcome is really ?Prime??
  A)
  0.5 done clear
  B)
  0.75 done clear
  C)
  0.6 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  n letters to each of which corresponds on addressed envelope are placed in the envelop at random. Then the probability that n letter is placed in the right envelope, will be:
  A)
  \[\frac{1}{1!}-\frac{1}{2!}+\frac{1}{3!}-\frac{1}{4!}+...{{(-1)}^{n}}\frac{1}{n!}\] done clear
  B)
  \[\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+...\frac{1}{n!}\] done clear
  C)
  \[\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+...{{(-1)}^{n}}\frac{1}{n!}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  In a sequence of independent trials, the probability of success on each trial is ¼. The probability that the second success occurs on the fourth or later trial, if the trials continue up to the second success only, is
  A)
  \[\frac{5}{32}\] done clear
  B)
  \[\frac{27}{32}\] done clear
  C)
  \[\frac{23}{32}\] done clear
  D)
  \[\frac{9}{32}\] done clear
  View Solution play_arrow

• question_answer15)
  Rajesh doesn't like to study. Probability that he will study is 1/3. If the studied then probability that he will fail is1/2 and if he didn?t study then probability that he will fail is 3/4 if in result Rajesh failed then what the probability that he didn't studies is.
  A)
  2/3 done clear
  B)
  3/4 done clear
  C)
  1/3 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, "the number is even", and B be the event, "the number is red" then;
  A)
  \[P(A)P(B)=\frac{1}{6}\] done clear
  B)
  A and B are independent done clear
  C)
  A and B are dependent done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  Two dice are thrown n times in succession. The probability of obtaining a double - six at least once is
  A)
  \[{{\left( \frac{1}{36} \right)}^{n}}\] done clear
  B)
  \[1-{{\left( \frac{35}{36} \right)}^{n}}\] done clear
  C)
  \[{{\left( \frac{1}{12} \right)}^{n}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  If the random variable X takes the values \[{{x}_{1}},{{x}_{2}},{{x}_{3}}...{{x}_{10}}\] with probabilities \[P(X={{x}_{i}})=ki,\]then the value of k is equal to
  A)
  \[\frac{1}{10}\] done clear
  B)
  \[\frac{1}{15}\] done clear
  C)
  \[\frac{1}{55}\] done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer19)
  6 coins are tossed together 64 times, if throwing a hand is considered as a success then the ex-pected frequency of at least 3 successes is
  A)
  64 done clear
  B)
  21 done clear
  C)
  32 done clear
  D)
  42 done clear
  View Solution play_arrow

• question_answer20)
  Rahul has to write a project, probability that he will get a project copy is ?P?, probability that he will get a blue pen is ?q? and probability that he will get a black pen is 1/2, if he can complete the project either with blue or with black pen or with both and probability that he completed the project is 1/2 then \[P(1+q)\]is 
  A)
  \[\frac{1}{2}\] done clear
  B)
  1 done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer21)
  A bag contains p white and q black ball. Two players A and B alternately draw a ball from the bag, replacing the balls each time after the draw till one of them draws a white ball and wins the game. If A begins the game and the probability of A winning the game is three times chat of B, then the ratio p:q is:
  A)
  3 : 4 done clear
  B)
  4 : 3 done clear
  C)
  2 : 1 done clear
  D)
  1 : 2    done clear
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• question_answer22)
              A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box. One at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is
  A)
  \[\frac{27}{32}\] done clear
  B)
  \[\frac{5}{64}\] done clear
  C)
  \[\frac{5}{32}\] done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer23)
  The probability of a man hitting a target is 1/4. The number of times he must shoot so that the probability he hits target, at least once is more than 0.9, is [use \[\log 4=0.602\,\,and\,\,\log 3=0.477\]]
  A)
  7 done clear
  B)
  8 done clear
  C)
  6 done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer24)
  Let \[{{E}^{c}}\] denote the complement of an event E. let E, F, G be pairwise independent events with \[P(G)>0\] and \[P(E\cap F\cap G)=0\]. Then \[P({{E}^{c}}\cap {{F}^{c}}/G)\] equals               
  A)
  \[P({{E}^{c}})+P({{F}^{c}})\] done clear
  B)
  \[P({{E}^{c}})-P({{F}^{c}})\] done clear
  C)
  \[P({{E}^{c}})-P(F)\] done clear
  D)
  \[P(E)-P({{F}^{c}})\] done clear
  View Solution play_arrow

• question_answer25)
  The mean and the variance of binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
  A)
  \[\frac{28}{256}\] done clear
  B)
  \[\frac{219}{256}\] done clear
  C)
  \[\frac{128}{256}\]        done clear
  D)
  \[\frac{37}{256}\] done clear
  View Solution play_arrow

• question_answer26)
  The probability of the simultaneous occurrence of two events A and B is p. if the probability that exactly one of the events occurs is q, then which of the following is not correct?
  A)
  \[P(A')+P(B')=2+2q-p\] done clear
  B)
  \[P(A')+P(B')=2-2p-q\] done clear
  C)
  \[P(A\cap B|A\cup B)=\frac{p}{p+q}\] done clear
  D)
  \[P(A'\cap B')=1-p-q.\] done clear
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• question_answer27)
  In a binomial distribution \[B\left( n,p=\frac{1}{4} \right)\], if the probability of at least one success is greater than or equal to \[\frac{9}{10}\], then n is greater than:
  A)
  \[\frac{1}{{{\log }_{10}}4+{{\log }_{10}}3}\] done clear
  B)
  \[\frac{9}{{{\log }_{10}}4-{{\log }_{10}}3}\] done clear
  C)
  \[\frac{4}{{{\log }_{10}}4-{{\log }_{10}}3}\] done clear
  D)
  \[\frac{1}{{{\log }_{10}}4-{{\log }_{10}}3}\] done clear
  View Solution play_arrow

• question_answer28)
  A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is
  A)
  \[1/4\] done clear
  B)
  \[1/3\] done clear
  C)
  \[2/3\]    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  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)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer30)
  The probability that a particular day in the month of July is a rainy day is ¾. Two person whose credibility are 4/5 and 2/3. Respectively, claim that 15 July was rainy day. The probability that it was really a rainy day is
  A)
  \[\frac{12}{13}\] done clear
  B)
  \[\frac{11}{12}\] done clear
  C)
  \[\frac{24}{25}\] done clear
  D)
  \[\frac{29}{30}\] done clear
  View Solution play_arrow

• question_answer31)
  The probability of India winning a test match against Westinies is \[\frac{1}{2}\]assuming independence from match to match the probability that in a 5 match series India?s second win occurs at the third test, is.
  A)
  2/3 done clear
  B)
  1/2 done clear
  C)
  1/4 done clear
  D)
  1/8 done clear
  View Solution play_arrow

• question_answer32)
  If \[{{E}_{1}}\] and \[{{E}_{2}}\] are two events such that \[P({{E}_{1}})=1/4,P({{E}_{2}}/{{E}_{1}})=1/2\] and \[P({{E}_{1}}/{{E}_{2}})=1/4\], then choose the incorrect statement.
  A)
  \[{{E}_{1}}and{{E}_{2}}\] are independent done clear
  B)
  \[{{E}_{1}}\] and \[{{E}_{2}}\] are exhaustive done clear
  C)
  \[{{E}_{2}}\] is twice as likely to occur as \[{{E}_{1}}\] done clear
  D)
  Probabilities of the events\[{{E}_{1}}\cap {{E}_{2}}\], \[{{E}_{1}}\] and \[{{E}_{2}}\] are in GP. done clear
  View Solution play_arrow

• question_answer33)
  A fair die is tossed eight times. The probability that a third six is observed on the eighth throw is
  A)
  \[^{7}{{C}_{2}}\frac{{{5}^{5}}}{{{6}^{8}}}\] done clear
  B)
  \[^{7}{{C}_{3}}\frac{{{5}^{3}}}{{{6}^{8}}}\] done clear
  C)
  \[^{7}{{C}_{6}}\frac{{{5}^{6}}}{{{6}^{8}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Probability that a man who is 40 year old, living till 75 years is 5/16, and another man who is 35 years old living till 70 years is 3/7 then what is the probability that at least one of them will be alive till 35 years hence?
  A)
  11/28 done clear
  B)
  19/28 done clear
  C)
  17/28 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  Let A and B be two events such that \[P(A\cap B')=0.20,P(A'\cap B)=0.15,\]\[P(A'\cap B')=0.1,\] Then \[P(A/B)\] is equal to
  A)
  11/14 done clear
  B)
  2/11 done clear
  C)
  2/7 done clear
  D)
  1/7 done clear
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• question_answer36)
  Three letters are written to three different persons and addresses on the three envelopes are also written. Without looking in the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{1}{3}\] done clear
  C)
  \[\frac{1}{6}\] done clear
  D)
  \[\frac{5}{6}\] done clear
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• question_answer37)
  A man and a woman appear in an interview for two vacancies in the same post. The probability of man?s selection is ¼ and that of the woman?s selection is 1/3. Then the probability that none of them will be selected is.
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{3}{4}\] done clear
  C)
  \[\frac{2}{3}\] done clear
  D)
  \[\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer38)
  If X follows a binomial distribution with parameter n=8 and \[p=\frac{1}{2}\], then \[P(\left| X-4 \right|\le 2)\] is
  A)
  \[\frac{119}{128}\]        done clear
  B)
  \[\frac{119}{228}\] done clear
  C)
  \[\frac{19}{128}\]          done clear
  D)
  \[\frac{18}{128}\] done clear
  View Solution play_arrow

• question_answer39)
  A random variable has the following probability distribution

  X:	0	1	2	3	4	5	6	7
  P(x)	0	2p	2p	3p	\[{{p}^{2}}\]	\[2{{p}^{2}}\]	\[7{{p}^{2}}\]	2p

  A)
  \[\frac{1}{10}\] done clear
  B)
  -1 done clear
  C)
  \[\frac{3}{10}\] done clear
  D)
  None done clear
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• question_answer40)
  Two aeroplane I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
  A)
  0.2 done clear
  B)
  0.7 done clear
  C)
  0.06 done clear
  D)
  0.14 done clear
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• question_answer41)
  A boy is throwing stones at a target. The probability of hitting the target at any trial is \[\frac{1}{2}\]. The probability of hitting the target 5th time at the 10th throw is:
  A)
  \[\frac{5}{{{2}^{10}}}\] done clear
  B)
  \[\frac{63}{{{2}^{9}}}\] done clear
  C)
  \[\frac{^{10}{{C}_{5}}}{{{2}^{10}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer42)
  There are n letters and n addressed envelopes, the probability that all the letters are not kept in the right envelope, is
  A)
   \[\frac{1}{n!}\] done clear
  B)
  \[1-\frac{1}{n!}\] done clear
  C)
  \[1-\frac{1}{n}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer43)
  Given two independent events, if the probability that exactly one of them occurs is \[\frac{26}{49}\] and the probability that none of them occurs is \[\frac{15}{49},\] then the probability of more probable of the two events is:
  A)
  4/7 done clear
  B)
  6/7 done clear
  C)
  3/7 done clear
  D)
  5/7 done clear
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• question_answer44)
  A man has bunch of 10 keys out of which only one can open the door. He chooses a key at random for opening the door. If at each trial the wrong key is discarded, then the probability that the door is opened on fifth trial is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{^{10}{{C}_{5}}}{{{10}^{5}}}\] done clear
  C)
  \[\frac{1}{10}\] done clear
  D)
  \[\frac{5!}{10!}\] done clear
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• question_answer45)
  If A and B are two events such that \[P(A)\ne 0\] and \[P(B)\ne 1,\] then \[P\left( \frac{\overline{A}}{\overline{B}} \right)=\]
  A)
  \[1-P\left( \frac{A}{B} \right)\] done clear
  B)
  \[1-P\left( \frac{\overline{A}}{B} \right)\] done clear
  C)
  \[\frac{1-P(A\cup B)}{P(\overline{B})}\] done clear
  D)
  \[\frac{P(\overline{A})}{P(\overline{B})}\] done clear
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• question_answer46)
  The mode of the binomial distribution for which mean and standard deviation are 10 and \[\sqrt{5}\] respectively is
  A)
  7 done clear
  B)
  8 done clear
  C)
  9 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer47)
  For k=1, 2, 3 the box \[{{B}_{k}}\] contains k red balls and \[(k+1)\] white balls. Let \[P({{B}_{1}})=\frac{1}{2},P({{B}_{2}})=\frac{1}{3}\]and \[P({{B}_{3}})=\frac{1}{6}.\] A box is selected at random and a ball is drawn from it, if a red ball is drawn, then the probability that it has come from box \[{{B}_{2}}\], is
  A)
  \[\frac{35}{78}\] done clear
  B)
  \[\frac{14}{39}\] done clear
  C)
  \[\frac{10}{13}\] done clear
  D)
  \[\frac{12}{13}\] done clear
  View Solution play_arrow

• question_answer48)
  3 friends A, B and C play the game ?Pahle hum pahle tum? in which they throw a die one after the other and the one who will get a composite number 1st will be announced as winner, if A started the game followed by B and then C then what is the ratio of their winning probabilities?
  A)
  \[9:6:4\] done clear
  B)
  \[8:6:5\] done clear
  C)
  \[10:5:4\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer49)
  A is one of 6 horses entered for a race, and is to be ridden by one of two jockeys B and C. it is 2 to 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, his chance of winning is trebled. What are the odds against winning of A?
  A)
  \[5:13\] done clear
  B)
  \[5:18\] done clear
  C)
  \[13:5\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer50)
  An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1st, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?
  A)
  \[0.6976\] done clear
  B)
  \[0.3024\] done clear
  C)
  0.72 done clear
  D)
  0.6431 done clear
  View Solution play_arrow

• question_answer51)
  A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is
  A)
  \[\frac{15}{{{2}^{8}}}\] done clear
  B)
  \[\frac{2}{15}\] done clear
  C)
  \[\frac{15}{{{2}^{13}}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  For two events A and B it is given that \[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\] and \[P\left( \frac{B}{A} \right)=\frac{1}{2}.\] Then,
  A)
  A and B are mutually exclusive events done clear
  B)
  A and B are dependent events done clear
  C)
  \[P\overline{\left( \frac{A}{b} \right)}=\frac{3}{4}\] done clear
  D)
  None of these done clear
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• question_answer53)
  One hundred identical coins, each with probability P of showing up heads, are tossed. If 0<p<1 and the probability of heads showing on 50 cons is equal to that of heads showing on 51 cons. The value of p is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{49}{101}\] done clear
  C)
  \[\frac{50}{101}\] done clear
  D)
  \[\frac{51}{101}\] done clear
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• question_answer54)
  In  from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is
  A)
  \[\frac{13}{32}\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{1}{32}\] done clear
  D)
  \[\frac{3}{16}\] done clear
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• question_answer55)
  In praxis business school Kolkata, 50% students like chocolate, 30% students like cake and 10% like booth. If a student is selected at random then what is the probability that he likes chocolates if it is known that he likes cake?
  A)
  1/3 done clear
  B)
  2/5 done clear
  C)
  3/5 done clear
  D)
  None of these done clear
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• question_answer56)
  The probability of guessing correctly at least 8 out of 10 answers on a true-false examination is
  A)
  \[\frac{5}{128}\] done clear
  B)
  \[\frac{19}{128}\] done clear
  C)
  \[\frac{11}{128}\] done clear
  D)
  \[\frac{7}{128}\] done clear
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• question_answer57)
  An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
  A)
  \[\frac{1}{10}\] done clear
  B)
  \[\frac{3}{10}\] done clear
  C)
  \[\frac{3}{5}\] done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer58)
  In an organization number of women are \[\mu \]times than that of men. If n things are distributed among them and the probability that the number of things Received by men are odd is\[\frac{1}{2}-{{\left( \frac{1}{2} \right)}^{n+1}}\], then \[\mu \] equal to
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  \[\frac{1}{4}\] done clear
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• question_answer59)
  Let \[0<P(A)<1,0<P(B)<1\] and \[P(A\cup B)=P(A)+P(B)-P(A)P(B,)\] then:
  A)
  \[P(B/A)=P(B)-P(A)\] done clear
  B)
  \[P(A'\cup B')=P(A')+P(B')\] done clear
  C)
  \[P(A\cap B)=P(A')P(B')\] done clear
  D)
  None of these done clear
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• question_answer60)
  A fair coin is tossed 99 times. If X is the number of times head occurs, \[P(X=r)\] is maximum when r is
  A)
  49 or 50 done clear
  B)
  50 or 51 done clear
  C)
  51 done clear
  D)
  None of these done clear
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• question_answer61)
  A box contains N cons, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is \[\frac{1}{2},\] while it is \[\frac{2}{3}\] when a biased coin is tossed. A coin is drawn from the box at random and it tossed twice. Then the probability that the coin drawn is fair, is
  A)
  \[\frac{9m}{8N+m}\] done clear
  B)
  \[\frac{9m}{8N-m}\] done clear
  C)
  \[\frac{9m}{8m-N}\] done clear
  D)
  \[\frac{9m}{8m+N}\]   done clear
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• question_answer62)
  By examining the chest X-ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. in a certain city, 1 in 1000 people suffers from TB, A  person is selected at random and is diagnosed to have TB. Then, the probability that the person actually has TB is
  A)
  \[\frac{110}{221}\] done clear
  B)
  \[\frac{2}{223}\] done clear
  C)
  \[\frac{110}{223}\]        done clear
  D)
  \[\frac{1}{221}\] done clear
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• question_answer63)
  In a book of 500 pages, it is found that there are 250 typing errors. Assume that Poisson law holds for the number of errors per page. Then, the probability that a random sample of 2 pages will contain no error, is
  A)
   \[{{e}^{-0.3}}\] done clear
  B)
  \[{{e}^{-0.5}}\] done clear
  C)
   \[{{e}^{-1}}\] done clear
  D)
  \[{{e}^{-2}}\] done clear
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• question_answer64)
  A problem in mathematics is given to three students, A, B, C and their respective probability of solving the problem is\[\frac{1}{2}\], \[\frac{1}{3}\]and\[\frac{1}{4}\]. Probability that the problem is solved is
  A)
  \[\frac{3}{4}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{2}{3}\] done clear
  D)
  \[\frac{1}{3}\] done clear
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• question_answer65)
  A and B are two independent witnesses (i.e there in no collision between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. The probability that the statement is true is
  A)
  \[\frac{x-y}{x+y}\] done clear
  B)
  \[\frac{xy}{1+x+y+xy}\] done clear
  C)
  \[\frac{x-y}{1-x-y+2xy}\] done clear
  D)
  \[\frac{xy}{1-x-y+2xy}\]   done clear
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• question_answer66)
  A bag contains n+1 cons. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is\[\frac{7}{12}\], then the value of n is.
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  None of these done clear
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• question_answer67)
  Abhay speaks the truth only 60%. Hasan rolls a die blindfolded and asks abhay to tell him if the outcome is a prime abhay says, YES what is the probability that he outcome is really prime?
  A)
  0.5 done clear
  B)
  0.75 done clear
  C)
  0.6 done clear
  D)
  None of these   done clear
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• question_answer68)
  A coin is tossed thrice. If E be the event of showing at least two heads and F be the event of showing head in the first throw, then find \[P\left( \frac{E}{F} \right)\]
  A)
  \[\frac{4}{3}\] done clear
  B)
  \[\frac{3}{4}\] done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  \[\frac{1}{2}\] done clear
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• question_answer69)
  A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is
  A)
  \[\frac{{{2}^{5}}{{.3}^{5}}}{{{5}^{10}}}\] done clear
  B)
  \[462\times {{\left( \frac{6}{25} \right)}^{5}}\] done clear
  C)
  \[231\times \frac{{{3}^{5}}}{{{5}^{10}}}\] done clear
  D)
  None of these done clear
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• question_answer70)
  For a biased dice, the probability for the different faces to turn up are

  Face	1	2	3	4	5	6
  P	0.01	0.32	0.21	0.15	0.05	0.147

  The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face, 1, is
  A)
  \[\frac{16}{21}\] done clear
  B)
  \[\frac{1}{10}\] done clear
  C)
  \[\frac{5}{16}\] done clear
  D)
  \[\frac{5}{21}\] done clear
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