Probability PYQs Set 10 (PDF)

Set 10 of 16 · Questions 271-300 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 10 (Q271-300)
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271. $Letters in the word HULULULU are rearranged. The probability of all three L being together is$ (1) $\frac{3}{20}$ (2) $\frac{2}{5}$ (3) $\frac{3}{28}$ (4) $\frac{5}{23}$ 272. $One card is selected at random from 27 cards numbered from 1 to 27 . What is the probability that the number on the card is even or divisible by 5 .$ (1) $\frac{15}{27}$ (2) $\frac{16}{27}$ (3) $\frac{17}{27}$ (4) $\frac{18}{27}$ 273. $If two cards are drawn at random simultaneously from a pack of 52 playing cards then the probability of getting a face card and a spade card other than the face card is$ (1) $\frac{35}{221}$ (2) $\frac{20}{221}$ (3) $\frac{77}{442}$ (4) $\frac{65}{442}$ 274. $If A and B are events having probabilities, P (A) = 0.6, P (B) = 0.4 and P (A \cap B) = 0, then probability that neither A nor B occurs is$ (1) $\frac{1}{4}$ (2) $1$ (3) $\frac{1}{2}$ (4) $0$ 275. $In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is -$ (1) $0$ (2) $\frac{400}{9} l oss$ (3) $\frac{400}{3} g ain$ (4) $\frac{400}{3} l oss$ 276. $A random variable X has following probability distribution X = x 123456 P (X = x) K 3 K 5 K 7 K 8 K K Then P (2 \leq X < 5) =$ (1) $3/5$ (2) $7/25$ (3) $23/25$ (4) $24/25$ 277. $Let A be a set of all 4 -digit natural numbers whose exactly one digit is 7 . Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is:$ (1) $\frac{1}{5}$ (2) $\frac{2}{9}$ (3) $\frac{97}{297}$ (4) $\frac{122}{297}$ 278. $Two dices are rolled. If both dices have six faces numbered 1,2,3,5,7 and 11 then the probability that the sumof the numbers on the top faces is less than or equal to 8 is:$ (1) $\frac{4}{9}$ (2) $\frac{17}{36}$ (3) $\frac{5}{12}$ (4) $\frac{1}{2}$ 279. $In a town the probability that a sick person may need to be admitted to an ICU is 10 % . If the probability that a person getting admitted to an ICU goes above 5 %, then the threat level is raised. The minimum percentage of the population of the town that should fall sick in order to raise the threat level is$ (1) $15$ (2) $30$ (3) $50$ (4) $70$ 280. $A pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in first throw and composite numbers on both the dice in second throw is$ (1) $\frac{1}{216}$ (2) $\frac{1}{16}$ (3) $\frac{1}{36}$ (4) $\frac{1}{9}$ 281. $In a random experiment a fair die is rolled until two fours are obtained in succession the probability that the experiment will end in the fifth throw of the die is equal$ (1) $\frac{200}{6 ^{5}}$ (2) $\frac{175}{6 ^{5}}$ (3) $\frac{150}{6 ^{5}}$ (4) $\frac{225}{6 ^{5}}$ 282. $Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N - 2, 3 N, N + 2 are in geometric progression be \frac{k}{48} . Then the value of k is$ (1) $2$ (2) $4$ (3) $16$ (4) $8$ 283. $Two players A and B are alternately throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is$ (1) $\frac{12}{23}$ (2) $\frac{11}{23}$ (3) $\frac{5}{119}$ (4) $\frac{12}{119}$ 284. $If an unbiased die, marked with - 2, - 1, 0, 1, 2, 3 on its faces, is through five times, then the probability that the product of the outcomes is positive, is:$ (1) $\frac{881}{2592}$ (2) $\frac{521}{2592}$ (3) $\frac{440}{2592}$ (4) $\frac{27}{288}$ 285. $If the roots of each of the equations 2 x^{2} + x - 1 = 0, 3 x^{2} - 10 x + 3 = 0 and 6 x^{2} + 11 x - 2 = 0 corresponds to probabilities of three events of a random experiment, then those events are$ (1) $equally likely$ (2) $exhaustive$ (3) $mutually exclusive$ (4) $mutually independent$ 286. $Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to \frac{31}{32}, then p lies in the interval$ (1) $(0, \frac{1}{2})$ (2) $(\frac{11}{12}, 1)$ (3) $(\frac{1}{2}, \frac{3}{4})$ (4) $(\frac{3}{4}, \frac{11}{12})$ 287. $Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to:$ (1) $\frac{32}{625}$ (2) $\frac{80}{243}$ (3) $\frac{40}{243}$ (4) $\frac{128}{625}$ 288. $In a book consisting of 600 pages, there are 60 typographical errors. The probability that a randomly chosen page will contain at most two errors, is$ (1) $\frac{1}{5} e$ (2) $\frac{1}{e ^{0.1}} (\frac{221}{200})$ (3) $\frac{1}{e ^{0.1}} (\frac{111}{200})$ (4) $\frac{1}{5} e^{0.1}$ 289. $In a bag there are 20 cards 10 names A and another 10 names B . Cards are drawn randomly one by one with replacement then find probability that second A comes before third B .$ (1) $\frac{13}{16}$ (2) $\frac{11}{16}$ (3) $\frac{7}{16}$ (4) $\frac{9}{16}$ 290. $Bag A contains 6 green and 8 red balls and bag B contains 9 green and 5 red balls. A card is drawn at random from a well shuffled pack of 52 playing cards. If it is a spade, two balls are drawn at random from bag A, otherwise two balls are drawn at random from bag B . If the two balls drawn are found to be of the same colour then the probability that they are drawn from bag A is$ (1) $\frac{43}{181}$ (2) $\frac{1}{4}$ (3) $\frac{48}{131}$ (4) $\frac{43}{138}$ 291. $Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is \frac{p}{q}, gcd (p, q) = 1, then p + q is equal to$ (1) $23$ (2) $24$ (3) $21$ (4) $22$ 292. $If X is a poisson variable such that 3 P (X = 4) = \frac{1}{2} P (X = 2) + P (X = 0), then the mean X is$ (1) $1$ (2) $2$ (3) $\frac{3}{2}$ (4) $\frac{1}{2}$ 293. $A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. Then, the probability that none of the balls drawn is blue is$ (1) $10/21$ (2) $11/21$ (3) $2/7$ (4) $5/7$ 294. $An integer is chosen at random from the integers 1, 2, 3, \dots, 50 . The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is$ (1) $\frac{8}{25}$ (2) $\frac{21}{50}$ (3) $\frac{9}{50}$ (4) $\frac{14}{25}$ 295. $A random variable X takes values 0, 1, 2, 3 with probabilities \frac{2 a + 1}{30}, \frac{8 a - 1}{30}, \frac{4 a + 1}{30}, b respectively, where a, b \in R . Let μ and σ respectively be the mean and standard deviation of X such that σ^{2} + μ^{2} = 2 . Then \frac{a}{b} is equal to:$ (1) $12$ (2) $30$ (3) $60$ (4) $3$ 296. $One card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is a face card (Jack, Queen and King only) is$ (1) $1/13$ (2) $3/13$ (3) $1/4$ (4) $9/52$ 297. $Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is$ (1) $\frac{1}{2}$ (2) $\frac{36}{55}$ (3) $\frac{6}{11}$ (4) $\frac{5}{11}$ 298. $A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is \frac{11}{50}, then n is equal to _________.$ 299. $25% of the population are smokers. A smoker has 27 times more changes to develop lung cancer then a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is \frac{k}{10} . then the value of k is _______$ 300. $A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is q. If p : q q=m : n, where m and n are coprime, then m+n is equal to$