Probability PYQs Set 12 (PDF)

Set 12 of 16 · Questions 331-360 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 12 (Q331-360)
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331. $A bag contains 2 n coins out of which n - 1 are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is \frac{41}{56 ^{’}} then the number of unfair coins in the bag is$ (1) $18$ (2) $15$ (3) $13$ (4) $14$ 332. $A die is thrown 10 times, the probability that an odd number will come up atleast one time is$ (1) $\frac{1023}{1024}$ (2) $\frac{11}{1024}$ (3) $\frac{1013}{1024}$ (4) $\frac{1}{1024}$ 333. $Let A and B be two events such that the probability that exactly one of them occurs is \frac{2}{5} and the probability that A or B occurs is \frac{1}{2} then the probability of both of them occur together is$ (1) $\frac{1}{10}$ (2) $\frac{2}{9}$ (3) $\frac{1}{8}$ (4) $\frac{1}{12}$ 334. $A man takes a step forward with probability 0.4 and one step backward with probability 0.6 , then the probability that at the end of eleven steps he is one step away from the starting point, is$ (1) $^{11} C_{6} \times (0.24)^{5}$ (2) $^{11} C_{6} \times (0.72)^{6}$ (3) $^{11} C_{5} \times (0.48)^{5}$ (4) $^{11} C_{5} \times (0.12)^{5}$ 335. $Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 29/45, then n is equal to:$ (1) $6$ (2) $3$ (3) $5$ (4) $4$ 336. $A fair coin is tossed 15 times. The probability that the tail will appear at least thrice is$ (1) $1 - \frac{10 ^{5}}{2 ^{15}}$ (2) $1 - \frac{121}{2 ^{15}}$ (3) $1 - \frac{1}{2 ^{15}}$ (4) $1 - \frac{16}{2 ^{15}}$ 337. $Let the sum of two positive integers be 24 . If the probability, that their product is not less than \frac{3}{4} times their greatest possible product, is \frac{m}{n}, where gcd (m, n) = 1, then n - m equals$ (1) $10$ (2) $9$ (3) $11$ (4) $8$ 338. $One ticket is selected at random from 50 tickets numbered 00, 01, 02, ....., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equal :$ (1) $\frac{1}{7}$ (2) $\frac{5}{14}$ (3) $\frac{1}{50}$ (4) $\frac{1}{14}$ 339. $If x is chosen at random from the set 1, 2, 3, 4 and y is chosen at random from the set 5, 6, 7, then the probability that xy will be even is$ (1) $\frac{5}{6}$ (2) $\frac{1}{6}$ (3) $\frac{1}{2}$ (4) $\frac{2}{3}$ 340. $If three numbers are drawn at random successively without replacement from a set S = 1, 2, \dots 10, then the probability that the minimum of the chosen numbers is 3 or their maximum is 7.$ (1) $\frac{11}{40}$ (2) $\frac{5}{40}$ (3) $\frac{3}{40}$ (4) $\frac{1}{40}$ 341. $A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is-$ (1) $\frac{2}{9}$ (2) $\frac{1}{9}$ (3) $\frac{2}{27}$ (4) $\frac{1}{27}$ 342. $Find the mean number of heads in three tosses of a fair coin.$ (1) $1.5$ (2) $2.5$ (3) $4.5$ (4) $3.5$ 343. $The range of a random variable X is 0, 1, 2 . If P (X = 0) = 3 C^{3}, P (X = 1) = 4 C - 10 C^{2} and P (X = 2) = 5 C - 1, then the value of C is$ (1) $\frac{2}{3}$ (2) $\frac{1}{3}$ (3) $\frac{5}{3}$ (4) $\frac{4}{3}$ 344. $When 3 dice are thrown at a time, the sum of the numbers appeared on 3 dice was found to be 15. Then the probability that the number 5 does not appear on any one of the dice is$ (1) $\frac{7}{10}$ (2) $\frac{3}{10}$ (3) $\frac{4}{15}$ (4) $\frac{2}{5}$ 345. $Let S = (w_{1} w_{2}, \dots) be the sample space associated to a random experiment. Let P (w_{n}) = \frac{P ( W _{n - 1} )}{2}, n \geq 2 . Let A = (2 k + 3 l; k, l ϵ N) and B = (w_{n}; n ϵ A) Then P (B) is equal to$ (1) $\frac{3}{32}$ (2) $\frac{3}{64}$ (3) $\frac{1}{16}$ (4) $\frac{1}{32}$ 346. $From out of 100 enrolled students, two sections of strength 40 and 60 are formed. If you and your friend are among those 100 students, then the probability that both of you are placed in the same section is$ (1) $\frac{^{98} C _{40} + ^{98} C _{58}}{^{100} C _{40}}$ (2) $\frac{^{40} C _{2} + ^{60} C _{2}}{^{100} C _{2}}$ (3) $\frac{^{98} C _{60} + ^{98} C _{38}}{^{100} C _{60}}$ (4) $\frac{^{98} C _{58} + ^{98} C _{0}}{^{100} C _{2}}$ 347. $A cube having edge of length 5 cm is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted is$ (1) $\frac{27}{125}$ (2) $\frac{4}{49}$ (3) $\frac{1}{8}$ (4) $\frac{8}{125}$ 348. $In a poison distribution, if P (X = 2) is twice P (X = 1), then the standard deviation of the distribution is$ (1) $1$ (2) $2$ (3) $4$ (4) $8$ 349. $If A and B are two events of a sample space S such that P (A) = 0.2, P (B) = 0.6 and P (A ∣ B) = 0.5, then P (A^{’} ∣ B) =$ (1) $3/10$ (2) $1/2$ (3) $2/3$ (4) $1/3$ 350. $A six faced die is biased such that 3 x P(a prime number) = 6 x p(a composite number) = 2 x p(1). Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :$ (1) $\frac{3}{11}$ (2) $\frac{5}{11}$ (3) $\frac{7}{11}$ (4) $\frac{8}{11}$ 351. $When a certain biased die is rolled, a particular face occurs with probability \frac{1}{6} - x and its opposite face occurs with probability \frac{1}{6} + x . All other faces occur with probability \frac{1}{6} . Note that opposite faces sum to 7 in any die. If 0 < x < \frac{1}{6}, and the probability of obtaining total sum=7, when such a die is rolled twice, is \frac{13}{96}, then the value of x is:$ (1) $\frac{1}{16}$ (2) $\frac{1}{8}$ (3) $\frac{1}{9}$ (4) $\frac{1}{12}$ 352. $A board has 16 squares as shown in the figure: Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is:$ (1) $7/10$ (2) $4/5$ (3) $23/30$ (4) $3/5$ 353. $Let Ajay will not appear in JEE exam with probability p = \frac{2}{7}, while both Ajay and Vijay will appear in the exam with probability q = \frac{1}{5} . Then the probability, that Ajay will appear in the exam and Vijay will not appear is :$ (1) $\frac{9}{35}$ (2) $\frac{18}{35}$ (3) $\frac{24}{35}$ (4) $\frac{3}{35}$ 354. $Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of X is :$ (1) $\frac{105}{16}$ (2) $\frac{7}{16}$ (3) $\frac{77}{36}$ (4) $\frac{49}{16}$ 355. $A signal which can be green or red with probability \frac{4}{5} and \frac{1}{5} respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is \frac{3}{4} . If the signal received at station B is green, then the probability that the original signal was green is$ (1) $\frac{3}{5}$ (2) $\frac{6}{7}$ (3) $\frac{20}{23}$ (4) $\frac{9}{20}$ 356. $Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :$ (1) $\frac{2}{7}$ (2) $\frac{1}{18}$ (3) $\frac{1}{7}$ (4) $\frac{1}{9}$ 357. $Let ω be a complex cube root of unity with ω \neq 1. A fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0 is$ (1) $\frac{1}{18}$ (2) $\frac{1}{9}$ (3) $\frac{2}{9}$ (4) $\frac{1}{36}$ 358. $Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is \frac{6}{11}, then n is equal to_____.$ (1) $13$ (2) $6$ (3) $4$ (4) $3$ 359. $It two different numbers are taken from the set {0,1,2,3,....., 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is$ (1) $\frac{6}{55}$ (2) $\frac{12}{55}$ (3) $\frac{14}{45}$ (4) $\frac{7}{55}$ 360. $Let the probability of getting head for a biased coin be \frac{1}{4} . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation 64 x^{2} +5Nx+1= 0 has no real root is \frac{p}{q}, where p and q are co-prime, then q - p is equal to..........$