Probability PYQs Set 7 (PDF)

Set 7 of 16 · Questions 181-210 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 7 (Q181-210)
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181. $A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is$ (1) $3/10$ (2) $1/5$ (3) $1/2$ (4) $4/5$ 182. $If A and B are two events such that P (A) = \frac{1}{2}, P (B) = \frac{1}{3} and P (A ∣ B) = \frac{1}{4}, then P (A^{’} \cap B^{’}) is$ (1) $\frac{1}{4}$ (2) $\frac{1}{12}$ (3) $\frac{3}{16}$ (4) $\frac{3}{4}$ 183. $If P (A) = 0.59, P (B) = 0.30 and P (A \cap B) = 0.21, then P (A^{’} \cap B^{’}) =$ (1) $0.11$ (2) $0.38$ (3) $0.32$ (4) $0.35$ 184. $An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :$ (1) $\frac{3}{16}$ (2) $\frac{1}{2}$ (3) $\frac{5}{16}$ (4) $\frac{1}{32}$ 185. $Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denote the number of defective oranges, then the variance of x is$ (1) $28/75$ (2) $18/25$ (3) $26/75$ (4) $14/25$ 186. $In a university campus, the probability that a person chosen at random is an engineering students is \frac{1}{5} . The probability of having at most two engineering students in a sample of 8 people is$ (1) $45 \times \frac{4 ^{6}}{5 ^{8}}$ (2) $17 \times \frac{4 ^{7}}{5 ^{8}}$ (3) $27 \times \frac{4 ^{6}}{5 ^{8}}$ (4) $19 \times \frac{4 ^{7}}{5 ^{8}}$ 187. $The mean and variance of a binomial distribution are 5 and 4 respectively. Then what is p (X = 1) = ?$ (1) $\frac{4 ^{24}}{5 ^{23}}$ (2) $\frac{4 ^{24}}{5 ^{24}}$ (3) $\frac{4}{5 ^{23}}$ (4) $\frac{4}{5 ^{24}}$ 188. $If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting tail on both the coins is$ (1) $(\frac{3}{4})^{50}$ (2) $(\frac{2}{3})^{50}$ (3) $(\frac{1}{3})^{50}$ (4) $(\frac{1}{2})^{50}$ 189. $Let A, B, C be pairwise independent events with P(c) > 0 and P (A \cap B \cap C) = 0. Then P (A^{c} \cap B^{c} / C) .$ (1) $1 - P(Bc)$ (2) $P(Ac) + P(Bc)$ (3) $P(Ac) - P(Bc)$ (4) $P(Ac) - P(b)$ 190. $In a test, a student either guesses or copies or knows the answer to a multiple choice question with four choices having one correct answer. The probability that he guesses the answer is \frac{1}{3} and the probability that he copies it is \frac{1}{12} . The probability that his answer is correct given that he copied it is \frac{1}{6} . The probability that he knew the answer, given that he has correctly answered it, is$ (1) $\frac{6}{7}$ (2) $\frac{15}{49}$ (3) $\frac{7}{12}$ (4) $\frac{10}{13}$ 191. $When two dice are thrown the probability of getting a prime number on one die and a composite number on the other is .$ (1) $\frac{1}{3}$ (2) $\frac{1}{4}$ (3) $\frac{1}{2}$ (4) $\frac{1}{6}$ 192. $If the mean and variance of a binomial distribution arc 4 and 2 respectively, then the probability of 2 successes of that binomial variate X, is$ (1) $\frac{1}{2}$ (2) $\frac{219}{256}$ (3) $\frac{37}{256}$ (4) $\frac{7}{64}$ 193. $A fair die with numbers 1 to 6 on their faces is thrown. Let X denote the number of factors of the number, on the uppermost face, then the probability distribution of X is$ (1) $X=x: 1, 2, 3, 4; P(X=x): \frac{1}{6}, \frac{1}{2}, \frac{1}{6}, \frac{1}{6}$ (2) $X=x: 1, 2, 3, 4; P(X=x): \frac{1}{6}, \frac{1}{6}, \frac{1}{6}, \frac{1}{2}$ (3) $X=x: 1, 2, 3, 4; P(X=x): \frac{1}{2}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}$ (4) $X=x: 1, 2, 3, 4; P(X=x): \frac{1}{6}, \frac{1}{6}, \frac{1}{2}, \frac{1}{6}$ 194. $A speaks truth in 75 % of the cases and B in 80 % of the cases. Then, the probability that their statements about an incident do not match, is$ (1) $\frac{7}{20}$ (2) $\frac{3}{20}$ (3) $\frac{2}{7}$ (4) $\frac{5}{7}$ 195. $If two dice are thrown and if X denotes the sum of the numbers that show up on the faces of the dice then the mean of the random variable X is$ (1) $\frac{27}{4}$ (2) $\frac{35}{6}$ (3) $\frac{41}{3}$ (4) $7$ 196. $In a class of 60 students, 40 opted for NCC 30 opted for NSS and 20 opted for both NCC and NSS . If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is:$ (1) $\frac{1}{6}$ (2) $\frac{1}{3}$ (3) $\frac{2}{3}$ (4) $\frac{5}{6}$ 197. $If the events A and B are independent if P (A^{’}) = \frac{2}{3} and P (B^{’}) = \frac{2}{7}, then P (A \cap B) is equal to$ (1) $\frac{4}{21}$ (2) $\frac{5}{21}$ (3) $\frac{1}{21}$ (4) $\frac{3}{21}$ 198. $Events E_{1} and E_{2} form a partition of the sample space S . A is any event such that P (E_{1}) = P (E_{2}) = \frac{1}{2}, P (E_{2} ∣ A) = \frac{1}{2} and P (A ∣ E_{2}) = \frac{2}{3}, then P (E_{1} ∣ A) is$ (1) $\frac{2}{3}$ (2) $1$ (3) $\frac{1}{4}$ (4) $\frac{1}{2}$ 199. $A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is$ (1) $\frac{1}{2}$ (2) $\frac{3}{4}$ (3) $\frac{3}{8}$ (4) $\frac{1}{8}$ 200. $Let α be a root of x^{2} + x + 1 = 0 and suppose that a fair die is thrown 3 times. If a, b and c are the numbers shown on the die, then the probability that α^{a} + α^{b} + α^{c} = 0, is$ (1) $\frac{2}{36}$ (2) $\frac{1}{27}$ (3) $\frac{1}{72}$ (4) $\frac{2}{9}$ 201. $If A and B are two events such that P (A) = 0.7, P (B) = 0.4 and P (A \cap B) = 0.5, where B denotes the complement of B, then P (B ∣ (A \cup B)) is equal to$ (1) $\frac{1}{3}$ (2) $\frac{1}{2}$ (3) $\frac{1}{4}$ (4) $\frac{1}{6}$ 202. $Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:$ (1) $\frac{1}{11}$ (2) $\frac{1}{10}$ (3) $\frac{1}{12}$ (4) $\frac{1}{17}$ 203. $The discreate random variables X and Y are independent from one another and are defined as X \sim B (n_{1}, 0.5) and Y \sim B (n_{2}, 0.4) . If the variance of both X and Y is 6 then n_{1} + n_{2} =$ (1) $7$ (2) $6$ (3) $5$ (4) $4$ 204. $If A and B are events such that P (A) = \frac{1}{4}, P (\frac{A}{B}) = \frac{1}{2} and P (\frac{B}{A}) = \frac{2}{3} then P (B) is$ (1) $\frac{2}{3}$ (2) $\frac{1}{6}$ (3) $\frac{1}{2}$ (4) $\frac{1}{3}$ 205. $If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is$ (1) $\frac{1}{6}$ (2) $\frac{13}{18}$ (3) $\frac{5}{36}$ (4) $\frac{5}{18}$ 206. $If P (\frac{A}{B}) = \frac{3}{10}, P (\frac{B}{A}) = \frac{4}{5} and P (A \cup B) = KP (B), then \frac{1}{K} is equal to$ (1) $\frac{40}{49}$ (2) $\frac{40}{43}$ (3) $\frac{100}{101}$ (4) $1$ 207. $The probability that a randomly chosen 5 -digit number is made from exactly two digits is:$ (1) $\frac{150}{10 ^{4}}$ (2) $\frac{134}{10 ^{4}}$ (3) $\frac{121}{10 ^{4}}$ (4) $\frac{135}{10 ^{4}}$ 208. $Suppose X has the following probability mass function P (X = 0) = 0.2, P (X = 1) = 0.5, P (X = 2) = 0.3 . What E (X^{2}) = ?$ (1) $2.89$ (2) $1.70$ (3) $1.10$ (4) $1.21$ 209. $A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective is$ (1) $\frac{9}{10}$ (2) $(\frac{1}{10})^{5}$ (3) $(\frac{9}{10})^{5}$ (4) $(\frac{1}{2})^{5}$ 210. $In a tournament, a team plays 10 matches with probabilities of winning and losing each match as \frac{1}{3} and \frac{2}{3} respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P (\| x - y \| \leq 2) is p, then 3^{9} p equals__________$