Probability PYQs Set 9 (PDF)

Set 9 of 16 · Questions 241-270 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 9 (Q241-270)
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241. $In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:$ (1) $\frac{200}{6 ^{5}}$ (2) $\frac{150}{6 ^{5}}$ (3) $\frac{225}{6 ^{5}}$ (4) $\frac{175}{6 ^{5}}$ 242. $From a collection of eight cards numbered 1 to 8 , if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is$ (1) $\frac{3}{14}$ (2) $\frac{6}{13}$ (3) $\frac{3}{16}$ (4) $\frac{1}{16}$ 243. $Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is$ (1) $\frac{2}{25}$ (2) $\frac{4}{25}$ (3) $\frac{2}{3}$ (4) $\frac{4}{75}$ 244. $The probability that A speaks truth is 4/5, while the probability that B speaks truth is 3/4 . Then the probability that A and B contradict each other, when asked to reveal the fact is$ (1) $\frac{3}{20}$ (2) $\frac{1}{5}$ (3) $\frac{7}{20}$ (4) $\frac{4}{5}$ 245. $If X is a Poisson variate satisfying the condition 3 P (x = 2) = P (x = 4) then P (x = 6) =$ (1) $\frac{162}{5 e ^{6}}$ (2) $\frac{108}{5 e ^{6}}$ (3) $\frac{324}{5 e ^{6}}$ (4) $\frac{648}{5 e ^{6}}$ 246. $A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. Theprobability that the missing card is not a spade, is :$ (1) $\frac{3}{4}$ (2) $\frac{52}{867}$ (3) $\frac{39}{50}$ (4) $\frac{22}{425}$ 247. $If X is a Poisson variate such that \frac{5}{3} k = P (X = 2) = P (X = 3), then P (X = 5) =$ (1) $k$ (2) $\frac{1}{4} k$ (3) $\frac{1}{2} k$ (4) $\frac{3}{4} k$ 248. $Let X denote the number of hours you study on a Sunday. Also it is known that P (X = x) = ⎩ ⎨ ⎧ 0.1, k x, 0, if x = 0 if x = 1 or 2 otherwise where k is a constant. What is the probability that you study atleast two hours?$ (1) $0.55$ (2) $0.15$ (3) $0.6$ (4) $0.3$ 249. $Two dice are rolled. If a random variable X is defined as the absolute difference of the two numbers that appear on them, then the mean of X is$ (1) $0$ (2) $\frac{13}{18}$ (3) $\frac{19}{9}$ (4) $\frac{35}{18}$ 250. $If the probability of hitting a target by a shooter, in anyshot, is \frac{1}{3}, then the minimum number of independentshots at the target required by him so that the probabilityof hitting the target at least once is greater than \frac{5}{6}, is:$ (1) $3$ (2) $6$ (3) $5$ (4) $4$ 251. $If 20 % of the bolts produced by a machine are defective then the probability that out of 4 bolts chosen at random, less than 2 bolts will be defective, is$ (1) $0.2048$ (2) $0.4096$ (3) $0.8192$ (4) $0.1024$ 252. $Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is$ (1) $\frac{1}{2}$ (2) $\frac{1}{3}$ (3) $\frac{2}{3}$ (4) $\frac{3}{4}$ 253. $If r.v. X : waiting time in minutes for bus and p.d.f. of X is given by f (x) = {\frac{1}{5}, 0, 0 \leq x \leq 5 otherwise then probability of waiting time not more than 4 minutes is$ (1) $0.3$ (2) $0.8$ (3) $0.2$ (4) $0.5$ 254. $Two number k_{1} and k_{2} are randomly chosen from the set of natural numbers. Then, the probability that the value of i^{k_{1}} + i^{k_{2}}, (i = - 1) is non-zero, equals$ (1) $\frac{1}{2}$ (2) $\frac{3}{4}$ (3) $\frac{1}{4}$ (4) $\frac{2}{3}$ 255. $A bag consists of 3 red balls, 5 blue balls and 8 green balls. A ball is selected at random. What is the probability of not getting a blue balls ?$ (1) $\frac{11}{16}$ (2) $\frac{3}{16}$ (3) $\frac{1}{2}$ (4) $\frac{5}{16}$ 256. $The probability that two randomly selected subsets of the set ∖ 1, 2, 3, 4, 5 ∖ have exactly two elements in their intersection, is:$ (1) $\frac{65}{2 ^{7}}$ (2) $\frac{135}{2 ^{9}}$ (3) $\frac{65}{2 ^{8}}$ (4) $\frac{35}{2 ^{7}}$ 257. $A box contains 6 red marbles numbers from 1 through 6 and 4 white marbles 12 through 15. Find the probability that a marble drawn 'at random' is white and odd numbered.$ (1) $1/5$ (2) $1/6$ (3) $5$ (4) $6$ 258. $If two cards are drawn simultaneously from a well shuffled pack of 52 cards, then the probability of getting a card having a prime number and a card having a number which is a multiple of 5 is$ (1) $\frac{94}{663}$ (2) $\frac{62}{663}$ (3) $\frac{30}{663}$ (4) $\frac{64}{663}$ 259. $If the probability of a bad reaction from a vaccination is 0.01 , then the probability that exactly two out of 300 people will get bad reaction is$ (1) $\frac{7}{2 e ^{3}}$ (2) $\frac{9}{2 e ^{3}}$ (3) $\frac{7}{e ^{3}}$ (4) $\frac{9}{e ^{3}}$ 260. $The probability of getting a success in a trail is five times that of a failure. The probability of getting at most one success in 5 trails, is$ (1) $\frac{25}{6 ^{5}}$ (2) $\frac{26}{6 ^{5}}$ (3) $(\frac{5}{6})^{5}$ (4) $2 (\frac{5}{6})^{5}$ 261. $If r . v . X \sim B (n = 5, p = \frac{1}{3}) then P (2 < X < 4) =$ (1) $\frac{80}{243}$ (2) $\frac{40}{243}$ (3) $\frac{40}{343}$ (4) $\frac{80}{343}$ 262. $A bag contains 21 toys numbered 1 to 21 . A toy is drawn and then another toy is drawn without replacement. The probability that both toys will show even numbers is$ (1) $\frac{5}{21}$ (2) $\frac{3}{14}$ (3) $\frac{11}{42}$ (4) $\frac{4}{21}$ 263. $A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is$ (1) $\frac{7}{5} (\frac{9}{10})^{4}$ (2) $\frac{7}{5} (\frac{9}{10})^{5}$ (3) $\frac{6}{5} (\frac{9}{10})^{4}$ (4) $\frac{6}{5} (\frac{9}{10})^{5}$ 264. $The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is$ (1) $\frac{129}{182}$ (2) $\frac{17}{26}$ (3) $\frac{19}{26}$ (4) $\frac{103}{182}$ 265. $Let a random variable X have a binomial distribution with mean 8 and variance 4 . If P (X \leq 2) = \frac{κ}{2 ^{16}} then k isequal to:$ (1) $17$ (2) $121$ (3) $1$ (4) $137$ 266. $Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition),then the probability that they are in A . P . with positive common difference, is:$ (1) $\frac{5}{101}$ (2) $\frac{10}{99}$ (3) $\frac{5}{33}$ (4) $\frac{15}{101}$ 267. $Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50 . A box is selected at random and a card is drawn from it. The number on the card is found to be a non-primenumber. The probability that the card was drawn from Box 1 is:$ (1) $\frac{4}{17}$ (2) $\frac{2}{3}$ (3) $\frac{2}{5}$ (4) $\frac{8}{17}$ 268. $From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a - b ⩾ 10 is \frac{m}{n}, gcd (m, n) = 1, then m + n is equal to____.$ 269. $Find the chance of throwing 10 exactly in one throw with 3 dice.$ 270. $From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of X is \frac{m}{n}, where gcd (m, n) = 1, then n - m is equal to________$