Probability PYQs Set 6 (PDF)

Set 6 of 16 · Questions 151-180 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 6 (Q151-180)
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151. $In a Binomial distribution B (n, p), if the mean and variance are 15 and 10 respectively, then the value of the parameter n is$ (1) $28$ (2) $16$ (3) $45$ (4) $25$ 152. $The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of 52 playing cards is$ (1) $\frac{1}{26}$ (2) $\frac{8}{221}$ (3) $\frac{2}{51}$ (4) $\frac{1}{52}$ 153. $If P (X = x) = c (\frac{2}{3})^{x}; x = 1, 2, 3, 4, \dots is a probability distribution function of a random variable X, then the value of c is$ (1) $\frac{1}{4}$ (2) $\frac{1}{3}$ (3) $\frac{1}{2}$ (4) $\frac{1}{6}$ 154. $Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2^{N} < N! is \frac{m}{n} where m and n are coprime, then 4m-3n is equal to$ (1) $6$ (2) $12$ (3) $10$ (4) $8$ 155. $A random variable X has the following probability distribution X = x_{i} : 123456789 P (X = x_{i}) : 10 k 9 k 8 k 8 k 6 k 5 k 4 k 3 k k where k is a real number If A = (x_{i} / x_{i}) is a prime number} and B = (x_{i} / x_{i} > 5) are two events, then P (A \cup B) =$ (1) $\frac{2}{3}$ (2) $\frac{4}{9}$ (3) $\frac{1}{27}$ (4) $\frac{5}{6}$ 156. $The coefficients a, b, c in the quadratic equation a x^{2} + bx + c = 0 are from the set 1, 2, 3, 4, 5, 6 . If the probability of this equation having one real root bigger than the other is p, then 216 p equals :$ (1) $57$ (2) $76$ (3) $38$ (4) $19$ 157. $Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:$ (1) $\frac{1}{2}$ (2) $\frac{1}{4}$ (3) $\frac{2}{3}$ (4) $\frac{1}{3}$ 158. $A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is$ (1) $\frac{11}{15}$ (2) $\frac{2}{15}$ (3) $\frac{3}{5}$ (4) $\frac{28}{75}$ 159. $For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = \frac{1}{4} and P (All the three events occur simultaneously) = \frac{1}{16} . Then the probability that at least one of the events occurs, is :$ (1) $\frac{7}{32}$ (2) $\frac{7}{16}$ (3) $\frac{7}{64}$ (4) $\frac{3}{16}$ 160. $Bag B_{1} contains 6 white and 4 blue balls, Bag B_{2} contains 4 white and 6 blue balls, and Bag B_{3} contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag B_{2}, is:$ (1) $\frac{4}{15}$ (2) $\frac{1}{3}$ (3) $\frac{2}{5}$ (4) $\frac{2}{3}$ 161. $Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white and 6 black balls is$ (1) $\frac{^{7} C _{3}}{^{12} C _{9}}$ (2) $\frac{7}{22}$ (3) $\frac{3}{22}$ (4) $\frac{7}{11}$ 162. $12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is$ (1) $\frac{^{12} C _{3} \times 2 ^{9}}{3 ^{12}}$ (2) $\frac{^{12} C _{3} \times 2 ^{9}}{3 ^{10}}$ (3) $\frac{^{12} C _{3}}{3 ^{12}}$ (4) $\frac{^{12} C _{3}}{3 ^{10}}$ 163. $A and B are two events such that P (A) \neq = 0, P (B / A) if (i) A is a subset of B (ii) A \cap B = φ are respectively$ (1) $1,1$ (2) $0,1$ (3) $0,0$ (4) $1,0$ 164. $A bag contains 5 red balls and 3 green balls. A ball is selected at random and not replaced. A second ball is then selected. The probability of selecting one red ball and one green ball is$ (1) $\frac{15}{112}$ (2) $\frac{15}{56}$ (3) $\frac{15}{64}$ (4) $\frac{15}{28}$ 165. $If the function p [x = x] = (\frac{K \cdot 2 ^{x}}{x !}, x = 0, 1, 2, 30, otherwise) forms p,m.f., then value of K is$ (1) $\frac{5}{19}$ (2) $\frac{1}{19}$ (3) $\frac{3}{19}$ (4) $\frac{2}{19}$ 166. $Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is$ (1) $\frac{1}{9}$ (2) $\frac{1}{18}$ (3) $\frac{1}{36}$ (4) $\frac{1}{12}$ 167. $An analysis of monthly wages paid to the workers of two jute mills A and B gives the following data: Mill-A Mill-B No. of workers 500600 Average daily wage (in rupees) 186175 Variance of distribution of wages 81100 Then$ (1) $wage bill of mill A is twice that of mill B$ (2) $mills A and B both have same wage bills.$ (3) $wage bill of mill A is greater than that of mill B$ (4) $wage bill of mill B is greater than that of mill A$ 168. $From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is$ (1) $\frac{67}{10 ^{8}}$ (2) $\frac{7}{10 ^{7}}$ (3) $\frac{81}{10 ^{8}}$ (4) $\frac{73}{10 ^{8}}$ 169. $If two sections of strengths 30 and 45 are formed from 75 students who are admitted in a school, then the probability that two particular students are always together in the same section is$ (1) $\frac{66}{185}$ (2) $\frac{19}{37}$ (3) $\frac{29}{185}$ (4) $\frac{18}{37}$ 170. $When two dice are rolled, let x be the probability of getting a sum of the numbers appear on the dice is at most 7. Let y be the probability of getting a sum 7 at least once when a pair of dice are rolled n times. In order to have y > x, the minimum n is$ (1) $3$ (2) $6$ (3) $5$ (4) $4$ 171. $A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is$ (1) $\frac{7}{34}$ (2) $\frac{8}{17}$ (3) $\frac{7}{16}$ (4) $\frac{7}{17}$ 172. $If X \sim B (n, p) with n = 10, p = 0.4 then E (X^{2}) =$ (1) $4$ (2) $2.4$ (3) $3.6$ (4) $18.4$ 173. $A die is thrown five times. If getting an odd number is a success, then the probability of getting at least 4 successes is$ (1) $\frac{1}{32}$ (2) $\frac{5}{32}$ (3) $\frac{13}{16}$ (4) $\frac{3}{16}$ 174. $If a Bernoulli trial is conducted n times, then Which one of the following is not suitable to use Poisson distribution? (i) Each trial results in two mutually exclusive outcomes namely success, failure (ii) The number ' n' of such trials is sufficiently large. (iii) The trails are independent of each other. (iv) The probability 'p' of success in each trial is very large.$ (1) $(iv)$ (2) $(iii)$ (3) $(ii)$ (4) $(i)$ 175. $There are 800 families with four children in each family. Assuming equal chance for every child to be a boy or a girl, the number of families expected to have children of both sexes is$ (1) $700$ (2) $100$ (3) $500$ (4) $300$ 176. $Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is$ (1) $\frac{1}{18}$ (2) $\frac{5}{18}$ (3) $\frac{1}{5}$ (4) $\frac{2}{5}$ 177. $A bag contains 9 identical black balls numbered 1 to 9 and 4 identical white balls numbered 1 to 4 . If 3 balls are drawn at a time randomly from that bag then the probability of getting at least one white ball is$ (1) $\frac{101}{143}$ (2) $\frac{7}{143}$ (3) $\frac{72}{143}$ (4) $\frac{42}{143}$ 178. $The probability distribution of a random variable is given below X = x P (X = x) 00 1 K 2 2 K 3 2 K 4 3 K 5 K^{2} 6 2 K^{2} 7 7 K^{2} + K Then, P (0 < x < 5) is equal to$ (1) $\frac{1}{10}$ (2) $\frac{3}{10}$ (3) $\frac{8}{10}$ (4) $\frac{7}{10}$ 179. $If ' 3 ' is the variance of Poisson distribution, then P (1 < x < 4) =$ (1) $\frac{123}{8} e^{- 3}$ (2) $3 e^{- 3}$ (3) $9 e^{- 3}$ (4) $(\frac{3 + 3}{2}) e^{- 3}$ 180. $The probability of a man hitting a target is \frac{1}{10} The least number of shots required, so that the probability of his hitting the target at least once is greater than \frac{1}{4} is$