Class 11 Mathematics Probability MCQs Set 14

Question. A fair coin is tossed repeatedly. If tail appears on the first four tosses then the probability of head appearing on fifth toss is
(a) 1/2
(b) 1/32
(c) 31/32
(d) 1/5
Answer: (a) 1/2

Question. In a shooting test, the probabilities for 3 persons A, B, C to hit the target are 1/2, 2/3 and 3/4. If all of them simultaneously aim at the target, the probability for exactly two persons hitting the target is
(a) 1/384
(b) 1/12
(c) 11/24
(d) 13/24
Answer: (c) 11/24

Question. A and B alternately throw a pair of symmetrical dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins, the probability of his winning is
(a) 11/36
(b) 30/61
(c) 31/61
(d) 1/36
Answer: (b) 30/61

Question. An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is
(a) 1/2
(b) 2/5
(c) 1/5
(d) 2/3
Answer: (b) 2/5

Question. The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match, the probability that in a 5 match series. India's second win occurs at third test is
(a) 1/8
(b) 1/4
(c) 1/2
(d) 2/3
Answer: (b) 1/4

Question. A bag contains 2 white, 3 black and 4 green balls. Two balls are drawn one after another with replacement. The probability that 1st one is white and second one is black is
(a) 5/27
(b) 1/9
(c) 2/27
(d) 4/27
Answer: (c) 2/27

Question. A bag contains 3 white, 2 black and 4 red balls. Three balls are drawn one after another with replacement at random. The probability of drawing a white, a black and a red ball in succession in that order is
(a) 1/21
(b) 5/21
(c) 8/243
(d) 2/243
Answer: (c) 8/243

Question. There are 6 red and 5 black balls in a bag. Two balls are drawn at random one after another with replacement. The probability that both the balls drawn may be red is
(a) 30/121
(b) 25/121
(c) 18/121
(d) 36/121
Answer: (d) 36/121

Question. In a group of equal number of men and women, 10% of men and 45% of women are unemployed. The probability that a person selected at random from that group is employed
(a) 11/40
(b) 29/40
(c) 18/40
(d) 9/40
Answer: (b) 29/40

Question. An urn A contains 8 black and 5 white balls. A second urn B contains 6 black and 7 white balls. A blind folded persons is asked to draw a ball selecting one of the urns, the probability that the ball drawn is white is
(a) 5/13
(b) 6/13
(c) 7/13
(d) 9/13
Answer: (b) 6/13

Question. One bag contains 5 white and 3 black balls and an other contains 4 white, 5 red balls. Two balls are drawn from one of them choosing at random. The probability that they are of different colours is
(a) 15/56
(b) 5/18
(c) 275/504
(d) 275/624
Answer: (c) 275/504

Question. A fair coin is tossed if the result is a head, a pair of fair dice is rolled and the score is noted. If the result is a tail, a card from a well shuffled pack of eleven numbered 1,2,3,.......11 is picked and the number on the card is noted. Then the probability that the number noted is either 7 or 8 is
(a) 45/512
(b) 193/792
(c) 193/1024
(d) 243/792
Answer: (b) 193/792

Question. If a randomly chosen year has 53 Sundays then probability that it is a non-leap year.
(a) 3/5
(b) 2/5
(c) 1/5
(d) 4/5
Answer: (a) 3/5

Question. The chance that Doctor A will diagonise disease X correctly is 60%. The chance that a patient will die by his treatment after correct diagnosis is 40% and the chance of death after wrong diagnosis is 70%. A patient of Doctor A who had disease X died. The probability that his disease was diagonised correctly is
(a) 5/13
(b) 6/13
(c) 2/13
(d) 7/13
Answer: (b) 6/13

Question. A bag contains 6 balls two balls are drawn and found them to be red. The probability that five balls in the bag are red
(a) 5/6
(b) 12/17
(c) 1/3
(d) 2/7
Answer: (d) 2/7

Question. A man is known to speak the truth 2 out of 3 times. He throws a die and reports that it is a six. The probability that it is actually a five is
(a) 3/8
(b) 1/7
(c) 2/7
(d) 4/5
Answer: (b) 1/7

Question. For k = 1,2,3 the box \( B_k \) contains k red balls and (k+1) white balls. Let \( P(B_1) = 1/2 \), \( P(B_2) = 1/3 \) and \( P(B_3) = 1/6 \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box \( B_2 \) is (Eamcet 2008)
(a) 35/78
(b) 14/39
(c) 10/13
(d) 12/13
Answer: (b) 14/39

Question. Box A contains 2 black and 3 red balls while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box, then the probability that it has come from box B is
(a) 21/41
(b) 10/31
(c) 12/31
(d) 13/41
Answer: (b) 10/31

Question. Let E be an event which is neither a certainty nor an impossibility. If probability is such that \( P(E) = 1 + \lambda + \lambda^2 \) and \( P(\overline{E}) = (1 + \lambda)^2 \) in terms of an unknown \( \lambda \) then \( P(E) \) is
(a) 1
(b) 3/4
(c) 1/4
(d) 1/2
Answer: (b) 3/4

Question. There are 10 pairs of shoes in a cupboard, out of which 4 shoes are picked out one by one randomly, the probability that there is at least one correct pair is
(a) 99/323
(b) 89/323
(c) 79/323
(d) 69/323
Answer: (a) 99/323

Question. If \( \frac{1+3p}{3}, \frac{1-p}{4} \) and \( \frac{1-2p}{2} \) are the probabilities of the three mutually exclusive events, then \( p \in \)
(a) \( [0,1] \)
(b) \( \left[0, \frac{1}{2}\right] \)
(c) \( \left[\frac{1}{3}, 1\right] \)
(d) \( \left[\frac{1}{3}, \frac{1}{2}\right] \)
Answer: (d) \( \left[\frac{1}{3}, \frac{1}{2}\right] \)

Question. There are 5 balls numbered 1 to 5 and 5 boxes numbered 1 to 5. The balls are kept in the boxes one in each box. The probability that exactly 2 balls are kept in the correspoinding numbered boxes and the remaining 3 balls in the wrong boxes, is
(a) 1/5
(b) 1/6
(c) 1/10
(d) 1/12
Answer: (b) 1/6

Question. A 2 x 2 matrix is formed with entries from the set {0, 1}. The probability it is singular is
(a) 3/16
(b) 1/8
(c) 5/8
(d) 5/16
Answer: (c) 5/8

Question. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant is negative is
(a) 3/16
(b) 3/8
(c) 5/8
(d) 7/8
Answer: (a) 3/16

Question. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant is non-zero is
(a) 3/16
(b) 3/8
(c) 5/8
(d) 7/8
Answer: (b) 3/8

Question. A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, MUMBAI. On the post mark only two consecutive letters AI are legible. The probability that it came from Mumbai is
(a) 39/190
(b) 42/149
(c) 39/191
(d) 38/191
Answer: (b) 42/149

Question. Four friends put their car keys on a table. when they leave the place, they picked up their keys at random. The probability that no persons picks his own key is
(a) 3/8
(b) 1/4
(c) 5/8
(d) 3/4
Answer: (a) 3/8

Question. If 5 cards letters as A, B, E, L and T shuffled placed one by one at random then probability of getting a word TABLE approximately is
(a) 0.008
(b) 0.8
(c) 0.08
(d) 0.0008
Answer: (a) 0.008

Question. If A and B are two independent events such that \( P(A) = \frac{1}{3} \) and \( P(B) = \frac{3}{4} \), then \( P\left\{\frac{B}{A \cup B}\right\} = \)
(a) 7/10
(b) 8/10
(c) 9/10
(d) 6/10
Answer: (c) 9/10

Question. A bag contains 6 white balls and 4 black balls. A ball is drawn and is put back in the bag with 5 balls of the same colour as that of the ball drawn. A ball is drawn again at random. The probability that the ball drawn now is white is
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
Answer: (c) 3/5

Question. Bag A contains 4 white and 7 black balls. Bag B contains 5 white and 6 black balls. A die is rolled. If 2 or 5 turns up then choose bag A otherwise choose bag B. If one ball is drawn at random from the selected bag, then the probability that it is black is
(a) 6/11
(b) 7/11
(c) 4/11
(d) 19/33
Answer: (d) 19/33

Question. A survey shows that in a certain village 2 out of every 100 men and 1 out of every 100 women have stomach ulcers. A person selected at random from the village is found to have stomach ulcer. The probability that the person is a male, given that the probability of selecting a male from the village is 0.55 is
(a) 22/31
(b) 1/2
(c) 1/3
(d) 11/31
Answer: (a) 22/31

Question. A bag contains 5 balls the colours of which are known. Two balls are drawn and found them to be red. The probability that all the balls in the bag are red is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/5
Answer: (a) 1/2

Question. A card from pack of 52 cards is lost. From the remaining cards of pack, two cards are drawn and are found to be spades. The probability of the missing card to be a spade is
(a) 1/50
(b) 3/50
(c) 6/50
(d) 11/50
Answer: (d) 11/50