Class 11 Mathematics Probability MCQs Set 11

Question. A magical die is so loaded that the probability of any face appearing is proportional to the number of points on its face. The probability of an odd number appearing is
(a) 2/7
(b) 3/7
(c) 4/7
(d) 5/7
Answer: (b) 3/7

Question. A die is loaded such that 6 turning upwards is twice as often as 1 and three times as any other face. The chance that we get a face with one point when we throw such a die is
(a) 6/17
(b) 3/17
(c) 2/17
(d) 5/17
Answer: (b) 3/17

Question. A fair die is thrown untill a face with less than 5 points is obtained. The probability of obtaining not less than 2 points on the last throw is
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1/8
Answer: (c) 3/4

Question. An ordinary die has four blank faces. One face marked 2, an other marked 3) Then the probability of obtaining a total of exactly 12 in 5 throws is
(a) \( \frac{15}{6^4} \)
(b) \( \frac{10}{6^4} \)
(c) \( \frac{5}{6^4} \)
(d) \( \frac{6}{6^4} \)
Answer: (c) \( \frac{5}{6^4} \)

Question. A and B throw a symmetrical die each. The odds against ‘ A’ not throwing a number greater than B is
(a) 1 to 5
(b) 5 to 1
(c) 7 to 5
(d) 5 to 7
Answer: (d) 5 to 7

Question. Three faces of a fair die are yellow, two faces red and one blue. The die is thrown twice. The probability that 1st throw will give an yellow face and the second a blue face is
(a) 1/6
(b) 1/9
(c) 1/12
(d) 1/3
Answer: (c) 1/12

Question. In a single throw with a pair of dice, the total score of occurrence for which the probability is maximum is
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (c) 7

Question. If three dice are thrown, then the probability that they show the numbers in A.P. is
(a) 1/36
(b) 1/18
(c) 2/9
(d) 5/18
Answer: (b) 1/18

Question. It is given that there are 52 Thursdays in a leap year. Then the probability that it will have 52 Fridays is
(a) 2/5
(b) 4/5
(c) 1/5
(d) 3/5
Answer: (b) 4/5

Question. Two children were picked at random and found to have been born in 1992 then the probability that exactly one of them is born on 29th February is
(a) 0
(b) \( \frac{1}{366 \times 183} \)
(c) \( \frac{365}{366 \times 183} \)
(d) \( \frac{731}{(366)^2} \)
Answer: (c) \( \frac{365}{366 \times 183} \)

Question. Five cards are drawn at random from a well shuffled pack of 52 playing cards. The probability that four of them may have the same face value is
(a) \( \frac{^{13}C_1 \times ^4C_1 \times ^{48}C_1}{^{52}C_5} \)
(b) \( \frac{^{13}C_1 \times ^{48}C_1}{^{52}C_5} \)
(c) \( \frac{^{13}C_5}{^{52}C_5} \)
(d) \( \frac{^{13}C_4 \times ^4C_1}{^{52}C_5} \)
Answer: (b) \( \frac{^{13}C_1 \times ^{48}C_1}{^{52}C_5} \)

Question. The probability of getting 9 cards of the same suit by a particular hand at a game of bridge is
(a) \( \frac{^{13}C_9}{^{52}C_{13}} \)
(b) \( \frac{^{13}C_9 \times ^{39}C_4}{^{52}C_{13}} \)
(c) \( \frac{^4C_1 \times ^{13}C_9 \times ^{39}C_4}{^{52}C_{13}} \)
(d) \( \frac{^4C_1 \times ^{13}C_9}{^{52}C_{13}} \)
Answer: (c) \( \frac{^4C_1 \times ^{13}C_9 \times ^{39}C_4}{^{52}C_{13}} \)

Question. In a hand at which the probability that 4 queens are held by a specified player is
(a) \( \frac{4 \times ^{48}C_9}{^{52}C_{13}} \)
(b) \( \frac{^{48}C_9}{^{52}C_{13}} \)
(c) \( \frac{4 \times ^{48}C_{13}}{^{52}C_{13}} \)
(d) \( \frac{2 \times ^{48}C_{13}}{^{52}C_{13}} \)
Answer: (b) \( \frac{^{48}C_9}{^{52}C_{13}} \)

Question. Two cards drawn one after another at random without replacement. The probability that both of them may have the same face value is
(a) 1/221
(b) 1/169
(c) 1/17
(d) 1/19
Answer: (c) 1/17

Question. Two cards are drawn at random from a pack of 52 cards. The probability of getting atleast a spade and an ace is
(a) 1/34
(b) 8/221
(c) 1/26
(d) 2/51
Answer: (c) 1/26

Question. The probability of getting different suit cards and different denomination cards when two cards are drawn from a pack is
(a) 13/17
(b) 13/34
(c) 12/17
(d) 6/17
Answer: (c) 12/17

Question. There are 3 cards. Each is painted red on one side and black on the other side. The cards are randomly placed in a row. The probability that no two consecutive cards show red is
(a) 3/8
(b) 5/8
(c) 5/6
(d) 1/8
Answer: (b) 5/8

Question. A bag contains 10 white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. The probability that the test will come to an end at the 7th draw is
(a) \( \frac{^{10}C_4 \times ^3C_2}{^{13}C_6} \times \frac{1}{7} \)
(b) \( \frac{^{10}C_4 \times ^3C_2}{^{13}C_6} \times \frac{2}{7} \)
(c) \( \frac{^{10}C_4 \times ^3C_2}{^{13}C_7} \)
(d) \( \frac{^{10}C_5 \times ^3C_2}{^{13}C_7} \)
Answer: (a) \( \frac{^{10}C_4 \times ^3C_2}{^{13}C_6} \times \frac{1}{7} \)

Question. Four tickets numbered 00, 01, 10, 11 are placed in a bag. A ticket is drawn at random and replaced. Again a ticket is drawn at random. The probability that the sum of the numbers on the tickets drawn is 21
(a) 1/4
(b) 1/8
(c) 1/16
(d) 1/12
Answer: (b) 1/8

Question. Two squares of a chess board having \( 8 \times 8 \) squares are selected at random the probability that they have a side in common is
(a) \( \frac{56}{^{64}C_2} \)
(b) \( \frac{112}{^{64}C_2} \)
(c) \( \frac{168}{^{64}C_2} \)
(d) \( \frac{268}{^{64}C_2} \)
Answer: (b) \( \frac{112}{^{64}C_2} \)

Question. If 16 squares of unit size are selected at random on a chess board, the probability that they form a square of \( 4 \times 4 \) is
(a) \( \frac{25}{^{64}C_{16}} \)
(b) \( \frac{25}{^{64}C_4} \)
(c) \( \frac{36}{^{64}C_{16}} \)
(d) \( \frac{36}{^{64}C_4} \)
Answer: (a) \( \frac{25}{^{64}C_{16}} \)

PROBLEMS ON ADDITION THEOREM

Question. Three numbers are chosen at random from {1,2,3,.....,10}. The probability that minimum of chosen number is 3 or maximum is 7, is
(a) 11/30
(b) 11/40
(c) 1/7
(d) 1/8
Answer: (b) 11/40

Question. Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one peron speaks Hindi only and the other speaks both Hindi and English is
(a) 3/5
(b) 7/12
(c) 1/5
(d) 2/5
Answer: (c) 1/5

Question. An electric bulb will last for 150 days or more with a probability 0.7 and it will last for at the most 160 days with probability 0.8. The probability that the bulb will last between 150 and 160 days is
(a) 0.1
(b) 0.3
(c) 0.5
(d) 0.4
Answer: (c) 0.5

PROBLEMS ON CONDITIONAL PROBABILITY

Question. If \( P(A) = \frac{3}{8}, P(B) = \frac{5}{8} \) & \( P(A \cap B) = \frac{1}{4} \), then \( P\left(\frac{\bar{A}}{B}\right) = \)
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
Answer: (c) 3/5

Question. For a biased die, the probability for different faces to turn up are given below:
Face : 1   2   3   4   5   6
Probability: 0.10   0.32   0.21   0.15   0.05   0.17
Such a die is tossed once and you are told that face 1 or 2 has turned up. The probability that it is face 1 is
(a) 16/21
(b) 5/21
(c) 4/7
(d) 3/7
Answer: (b) 5/21

Question. Two dice are thrown. The probability of getting a sum of 7 points, if it is known that the two dice are showing different numbers is
(a) 1/6
(b) 1/5
(c) 1/4
(d) 1/8
Answer: (b) 1/5

Question. Two symmetrical dice are rolled. If the numbers thrown up on them are different, the probability of getting an even number as the sum of the numbers is
(a) 1/5
(b) 2/5
(c) 3/5
(d) 4/5
Answer: (b) 2/5

Question. Three dice are rolled. If no two dice show the same face, the probability that one is an ace
(a) 1/4
(b) 1/3
(c) 1/2
(d) 1/8
Answer: (c) 1/2

Question. In selecting 2 cards one at a time with replacement from a deck, the probability that the second card is an ace, given that the 1st card was a face card is
(a) 1/13
(b) 2/13
(c) 3/13
(d) 4/13
Answer: (a) 1/13

Question. One ticket is selected randomly from the set of 100 tickets numbered as {00, 01, 02, 03, 04,05,........,98, 99}. E₁ and E₂ denote the sum and product of the digits of the number of the selected ticket. The value of \( P \left( \frac{E_1 = 9}{E_2 = 0} \right) \) is
(a) 1/19
(b) 2/19
(c) 3/19
(d) 1/18
Answer: (b) 2/19

Question. A piece of equipment will function when all the three components A, B, C are working. The probability of A failing during one year is 0.15 that of B is 0.05 and that of C is 0.10. The probability that the equipment will fail before the end of the year is
(a) 0.72675
(b) 0.27325
(c) 1
(d) 0.95
Answer: (b) 0.27325

Question. A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken together. If one of them is found to be good, the probability that the other is rotten is
(a) 5/13
(b) 7/13
(c) 8/13
(d) 9/13
Answer: (c) 8/13

PROBLEMS ON INDEPENDENT EVENTS

Question. Let A and B be two events such that \( P(\overline{A \cup B}) = \frac{1}{6}, P(A \cap B) = \frac{1}{4} \) and \( P(\bar{A}) = \frac{1}{4} \) Then events A and B are (JEE MAIN 2014)
(a) equally likely, but not independent
(b) equally likely and mutually exclusive
(c) mutually exclusive and independent
(d) independent but not equally likely
Answer: (d) independent but not equally likely

Question. A candidate takes three tests in succession and the probability of passing the first test is p. The probability of passing each succeeding test is p or \( \frac{p}{2} \) according as he passes or fails in the preceding one. The candidate is selected if he passes at least two tests. The probability that the candidate is selected is (EAM-2014)
(a) \( p(2-p) \)
(b) \( p + p^2 + p^3 \)
(c) \( p^2(1-p) \)
(d) \( p^2(2-p) \)
Answer: (d) \( p^2(2-p) \)

Question. A coin is biased so that the probability of falling head when tossed is 1/4. If the coin is tossed 5 times the probability of obtaining 2 heads and 3 tails, with heads occuring in succession is
(a) \( \frac{5 \times 3^3}{4^5} \)
(b) \( \frac{3^3}{5^4} \)
(c) \( 2 \left( \frac{3}{8} \right)^3 \)
(d) \( \frac{3^3}{4^5} \)
Answer: (c) \( 2 \left( \frac{3}{8} \right)^3 \)

Question. The probability that a teacher will give a surprise test during any class meeting is 3/5. If a student is absent on two days, then the probability that he will miss at least one test is
(a) 9/25
(b) 4/25
(c) 21/25
(d) 13/25
Answer: (c) 21/25

Question. A person draws a card from a well shuffled pack of 52 playing cards. Replaces it and shuffles the pack. He continues doing so until he draws a spade. The chance that he fails first two times is
(a) 1/16
(b) 9/16
(c) 9/64
(d) 9/32
Answer: (b) 9/16

Question. A symmetrical die is thrown 1st and secondly two symmetrical dice are thrown together. The probability that 1st throw was a face with 6 points upward & the second throw was a sum of 6 points
(a) 1/36
(b) 5/36
(c) 5/216
(d) 1/216
Answer: (c) 5/216

Question. A box contains 2 black, 3 white, 4 red balls. One ball is drawn at random and kept aside. From the remaining balls another ball is drawn and kept aside the first. The process is repeated till all the balls are drawn from the box. The probability that balls drawn are in the sequence of 2 black, 3 white, 4 red balls is
(a) \( \frac{^2c_2 \cdot ^3c_3 \cdot ^4c_4}{^9c_3} \)
(b) 1/1260
(c) 1/180
(d) 1/630
Answer: (b) 1/1260