Probability PYQs Set 5 (PDF)

Set 5 of 16 · Questions 121-150 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 5 (Q121-150)
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121. $If a die is rolled three times, then the probability of getting a larger number on its face than the previous number each time, is$ (1) $\frac{15}{216}$ (2) $\frac{5}{54}$ (3) $\frac{13}{216}$ (4) $\frac{1}{18}$ 122. $The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 is$ (1) $\frac{5}{16}$ (2) $\frac{8}{16}$ (3) $\frac{11}{16}$ (4) $\frac{1}{16}$ 123. $If three unbiased dice are rolled simultaneously then the probability that all the three dice show distinct numbers is$ (1) $\frac{1}{36}$ (2) $\frac{35}{36}$ (3) $\frac{5}{9}$ (4) $\frac{4}{9}$ 124. $If the standard deviation of the random variable X is 3 pq and mean is 3 p then E (X^{2}) =$ (1) $3 pq + 3 q^{2}$ (2) $3 p (1 + 2 p)$ (3) $3 pq + 3 p^{2}$ (4) $3 q (1 + 2 q)$ 125. $A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails, then P (X = 1) =$ (1) $\frac{1}{2}$ (2) $\frac{2}{3}$ (3) $\frac{1}{6}$ (4) $\frac{3}{4}$ 126. $A seven digit number is formed using digit 3, 3, 4, 4, 4, 5, 5 . The probability, that number so formed is divisible by 2, is :$ (1) $\frac{6}{7}$ (2) $\frac{4}{7}$ (3) $\frac{3}{7}$ (4) $\frac{1}{7}$ 127. $A random variable X has the following probability distribution: X 12345 P (x) K^{2} 2 k K 2 K 5 K^{2} Then P (x > 2) is equal to:$ (1) $\frac{23}{36}$ (2) $\frac{7}{12}$ (3) $\frac{1}{36}$ (4) $\frac{1}{6}$ 128. $A die is thrown four times. The probability of getting perfect square in at least one throw is$ (1) $\frac{16}{81}$ (2) $\frac{65}{81}$ (3) $\frac{23}{81}$ (4) $\frac{58}{81}$ 129. $A box contains 6 pens, 2 of which are defective. Two pens are taken randomly from the box. If r.v. X : Number of defective pens obtained, then standard deviation of X =$ (1) $\pm \frac{4}{3 5}$ (2) $\frac{8}{3}$ (3) $\frac{16}{45}$ (4) $\frac{4}{3 5}$ 130. $Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations. x + y + z=1 2x + Ny + 2z = 2 3x + 3y + Nz =3 has unique solution is \frac{k}{6}, then te sum of value of k and all possible values of N is$ (1) $18$ (2) $19$ (3) $20$ (4) $21$ 131. $From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is$ (1) $\frac{1}{15}$ (2) $\frac{25}{57}$ (3) $\frac{35}{256}$ (4) $\frac{1}{221}$ 132. $If A and B are two events such that P (A / B) = 0.6, P (B / A) = 0.3 and P (A) = 0.1, then P (A ˉ \cap B ˉ) equals$ (1) $0.88$ (2) $0.12$ (3) $0.6$ (4) $0.4$ 133. $2 n unbiased coins are tossed. The probability of having the number of heads is not equal to the number of tails, is$ (1) $\frac{2 n !}{( n ! ) ^{2}} (\frac{1}{2})^{2 n}$ (2) $1 - \frac{2 n !}{( n ! ) ^{2}}$ (3) $\frac{2 n !}{( n ! ) ^{2}}$ (4) $1 - \frac{2 n !}{( n ! ) ^{2}} \cdot \frac{1}{4 ^{n}}$ 134. $In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is$ (1) $\frac{7}{12}$ (2) $\frac{5}{36}$ (3) $\frac{5}{12}$ (4) $\frac{7}{36}$ 135. $A bag contains 10 balls out of which k are red and (10 - k) are black, where 0 \leq k \leq 10 . If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:$ (1) $\frac{14}{55}$ (2) $\frac{7}{55}$ (3) $\frac{7}{110}$ (4) $\frac{7}{11}$ 136. $A and B are mutually exclusive events of a random experiment and P (B) \neq = 1, then P (A ∣ B^{c}) =$ (1) $\frac{P ( A )}{1 - P ( B )}$ (2) $\frac{P ( B )}{1 - P ( A )}$ (3) $\frac{P ( A )}{1 + P ( B )}$ (4) $\frac{P ( A )}{P ( A ) + P ( B )}$ 137. $The probability of occurrence of an event is \frac{2}{5} and the probability of non-occurrence of another event is \frac{3}{10} . If these events are independent, then the probability that only one of the two events occur is$ (1) $\frac{27}{25}$ (2) $\frac{27}{50}$ (3) $\frac{7}{25}$ (4) $\frac{14}{25}$ 138. $In a Poisson distribution with unit mean, \sum_{x = 0}^{\infty} ∣ x - x ˉ ∣ P (X = x) = (x ˉ is the mean of the distribution)$ (1) $e$ (2) $\frac{1}{e}$ (3) $\frac{2}{e}$ (4) $\frac{2}{3 e}$ 139. $There are 10 coins in a box out of which 8 are normal and the remaining are with heads on both sides. A coin is chosen at random from the box and tossed 6 times. If it shows heads each time, then the probability that the selected coin has head on both sides is$ (1) $\frac{16}{17}$ (2) $\frac{32}{41}$ (3) $\frac{8}{9}$ (4) $\frac{12}{13}$ 140. $The probability distribution of x is x 0123 P (x) 0.2 k k 2 k Find the value of k .$ (1) $0.3$ (2) $0.1$ (3) $0.2$ (4) $0.4$ 141. $The probability of happening of an event A is 0.5 and that of B is 0.3 . If A and B are mutually exclusive events, then the probability of neither A nor B is$ (1) $0.4$ (2) $0.5$ (3) $0.2$ (4) $0.9$ 142. $Two cards are drawn at random one after the other with replacement from a pack of 52 playing cards. Then the variance of the random variable of the number of spade cards among the drawn cards is$ (1) $\frac{3}{8}$ (2) $\frac{1}{2}$ (3) $\frac{5}{8}$ (4) $\frac{7}{8}$ 143. $If A and B are mutually exclusive events, given that P (A) = \frac{3}{5}, P (B) = \frac{1}{5}, then P (A or B) is$ (1) $0.8$ (2) $0.6$ (3) $0.4$ (4) $0.2$ 144. $A coin is tossed three times. Let X denote the number of times a tail follows a head. If μ and σ^{2} denote the mean and variance of X, then the value of 64 (μ + σ^{2}) is:$ (1) $51$ (2) $64$ (3) $32$ (4) $48$ 145. $If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is:$ (1) $\frac{16065}{2 ^{15}}$ (2) $\frac{965}{2 ^{10}}$ (3) $\frac{945}{2 ^{10}}$ (4) $\frac{945}{2 ^{11}}$ 146. $If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i^{th} roll than the number obtained in the (i - 1)^{th} roll, i = 2, 3, is equal to$ (1) $3/54$ (2) $2/54$ (3) $1/54$ (4) $5/54$ 147. $During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6 . The probability that in a given week there will be exactly two days with severe fog is$ (1) $\frac{6048}{5 ^{7}}$ (2) $\frac{2016}{5 ^{7}}$ (3) $\frac{3024}{5 ^{7}}$ (4) $\frac{12096}{5 ^{7}}$ 148. $A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and almost one is defective is$ (1) $\frac{9}{10}$ (2) $\frac{1}{2} (\frac{9}{10})^{4}$ (3) $(\frac{9}{10})^{5} + \frac{1}{2} (\frac{9}{10})^{4}$ (4) $\frac{1}{2} (\frac{9}{10})^{5}$ 149. $Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively$ (1) $\frac{6}{11}, \frac{5}{11}$ (2) $\frac{5}{11}, \frac{6}{11}$ (3) $\frac{8}{11} \frac{3}{11}$ (4) $\frac{3}{11}, \frac{8}{11}$ 150. $A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn at random. The probability that they are not of same colour is$ (1) $\frac{37}{44}$ (2) $\frac{31}{44}$ (3) $\frac{21}{44}$ (4) $\frac{41}{44}$