Class 11 Mathematics Probability MCQs Set 08

Question. Two uniform dice marked 1 to 6 are thrown together. The probability that the total score on them is either minimum or maximum.
(a) \( \frac{4}{36} \)
(b) \( \frac{5}{36} \)
(c) \( \frac{2}{36} \)
(d) \( \frac{1}{36} \)
Answer: (c) \( \frac{2}{36} \)

Question. Two uniform dice marked 1 to 6 are thrown together. The probability that the score on the two dice is at least seven is
(a) \( \frac{5}{12} \)
(b) \( \frac{7}{12} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{1}{2} \)
Answer: (b) \( \frac{7}{12} \)

Question. Two uniform dice marked 1 to 6 are thrown together. The probability that the sum is even is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{12} \)
Answer: (c) \( \frac{1}{2} \)

Question. Two dice are thrown. The probability that the absolute difference of points on them is 4 is
(a) \( \frac{1}{7} \)
(b) \( \frac{1}{8} \)
(c) \( \frac{1}{9} \)
(d) \( \frac{1}{6} \)
Answer: (c) \( \frac{1}{9} \)

Question. Three symmetrical dice are thrown. The probability of having different points on them is
(a) \( \frac{35}{36} \)
(b) \( \frac{4}{9} \)
(c) \( \frac{5}{9} \)
(d) \( \frac{1}{36} \)
Answer: (c) \( \frac{5}{9} \)

Question. A and B throw with 3 dice. If A throws a sum of 16 points, the probability of B throwing a higher sum is
(a) \( \frac{7}{54} \)
(b) \( \frac{5}{54} \)
(c) \( \frac{1}{54} \)
(d) \( \frac{3}{54} \)
Answer: (c) \( \frac{1}{54} \)

Question. On a symmetrical die the numbers 1, -1, 2, -2, 3 and 0 are marked on its 6 faces. If such a die is thrown 3 times, the probability that the sum of points on them is 6 is
(a) \( \frac{5}{27} \)
(b) \( \frac{5}{54} \)
(c) \( \frac{5}{108} \)
(d) \( \frac{3}{108} \)
Answer: (c) \( \frac{5}{108} \)

Question. A symmetrical die is thrown 4 times. The probability that 3 and 6 will turn up exactly 2 times each is
(a) \( \frac{1}{6^{4}} \)
(b) \( \frac{1}{6^{3}} \)
(c) \( \frac{1}{6^{2}} \)
(d) \( \frac{1}{6} \)
Answer: (b) \( \frac{1}{6^{3}} \)

Question. Two symmetrical dice are thrown. The probability of throwing a doublet such that their sum is greater than 9 is
(a) \( \frac{1}{36} \)
(b) \( \frac{1}{18} \)
(c) \( \frac{1}{9} \)
(d) \( \frac{1}{72} \)
Answer: (b) \( \frac{1}{18} \)

Question. Two symmetrical dice are rolled. The probability that sum of the points on them is divisible by 5 is
(a) \( \frac{2}{9} \)
(b) \( \frac{4}{9} \)
(c) \( \frac{7}{36} \)
(d) \( \frac{5}{9} \)
Answer: (c) \( \frac{7}{36} \)

Question. Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6) and let \( E_{k} = \{(a,b) \in S : ab = k \} \) for \( k \geq 1 \) If \( p_{k} = P(E_{k}) \) for \( k \geq 1 \) then correct among the following, is
(a) \( p_{1} < p_{30} < p_{4} < p_{6} \)
(b) \( p_{36} < p_{6} < p_{2} < p_{4} \)
(c) \( p_{1} < p_{11} < p_{4} < p_{6} \)
(d) \( p_{36} < p_{11} < p_{6} < p_{4} \)
Answer: (a) \( p_{1} < p_{30} < p_{4} < p_{6} \)

Question. A coin and a six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is
(a) \( 1/2 \)
(b) \( 3/4 \)
(c) \( 1/4 \)
(d) \( 2/3 \)
Answer: (c) \( 1/4 \)

Question. Six faces of a unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is
(a) \( 5/18 \)
(b) \( 5/36 \)
(c) \( 13/18 \)
(d) \( 25/36 \)
Answer: (a) \( 5/18 \)

Question. The probability that a leap year will have 53 Sundays and 53 Mondays is
(a) \( \frac{3}{7} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{1}{7} \)
(d) \( \frac{4}{7} \)
Answer: (c) \( \frac{1}{7} \)

Question. The probability that the February of a leap year will have 5 saturdays is
(a) \( \frac{3}{7} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{1}{7} \)
(d) \( \frac{4}{7} \)
Answer: (c) \( \frac{1}{7} \)

Question. The probability that 13th day of the randomly chosen month is a Friday is
(a) \( \frac{1}{7} \)
(b) \( \frac{1}{12} \)
(c) \( \frac{1}{84} \)
(d) \( \frac{1}{42} \)
Answer: (c) \( \frac{1}{84} \)

Question. In a non leap year the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays
(a) \( \frac{1}{7} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{3}{7} \)
(d) \( \frac{4}{7} \)
Answer: (c) \( \frac{3}{7} \)

Question. It is given that a leap year has 53 Sundays, the probability that it has 53 Mondays is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{7} \)
(c) \( \frac{6}{7} \)
(d) \( \frac{2}{7} \)
Answer: (a) \( \frac{1}{2} \)

Question. A pack of cards is distributed among four hands equally. The probability that 5 spades, 3 clubs, 3 hearts and the rest diamonds may be in a particular hand is
(a) \( \frac{^{4}c_{1} \times ^{13}c_{5} \times ^{13}c_{3} \times ^{13}c_{2}}{^{52}c_{13}} \)
(b) \( \frac{^{13}c_{5} \times ^{26}c_{6} \times ^{13}c_{2}}{^{52}c_{13}} \)
(c) \( \frac{^{13}c_{5} \times ^{13}c_{3} \times ^{13}c_{3} \times ^{13}c_{2}}{^{52}c_{13}} \)
(d) \( \frac{^{4}c_{1} \times ^{13}c_{3} \times ^{13}c_{3} \times ^{13}c_{2}}{^{52}c_{13}} \)
Answer: (c) \( \frac{^{13}c_{5} \times ^{13}c_{3} \times ^{13}c_{3} \times ^{13}c_{2}}{^{52}c_{13}} \)

Question. A card is drawn from an ordinary pack of 52 playing cards and a gambler bets it as a spade or an ace. The probability that he wins the bet is
(a) \( \frac{2}{13} \)
(b) \( \frac{3}{13} \)
(c) \( \frac{4}{13} \)
(d) \( \frac{1}{13} \)
Answer: (c) \( \frac{4}{13} \)

Question. In shuffling a pack of cards, four cards are accidentally dropped. The probability that the cards dropped are one from each suit is
(a) \( \frac{^{13}c_{4}}{^{52}c_{4}} \)
(b) \( \frac{13^{4}}{^{52}c_{4}} \)
(c) \( \frac{^{13}c_{4}}{13^{4}} \)
(d) \( \frac{13!}{^{52}c_{4}} \)
Answer: (b) \( \frac{13^{4}}{^{52}c_{4}} \)

Question. The face cards are removed from a well shuffled pack of 52 cards. Out of the remaining cards 4 are drawn at random. The probability that they belong to different suits is
(a) \( \frac{13^{4}}{^{52}c_{4}} \)
(b) \( \frac{^{13}c_{4}}{^{40}c_{4}} \)
(c) \( \frac{10^{4}}{^{40}c_{4}} \)
(d) \( \frac{13^{4}}{^{40}c_{4}} \)
Answer: (c) \( \frac{10^{4}}{^{40}c_{4}} \)

Question. In a game of bridge, the probability of a particular player having all the 13 cards of red colour is
(a) \( \frac{13^{4}}{^{52}c_{13}} \)
(b) \( \frac{^{26}c_{13}}{^{52}c_{13}} \)
(c) \( \frac{13 \times 4}{^{52}c_{13}} \)
(d) \( \frac{13^{2}}{^{52}c_{13}} \)
Answer: (b) \( \frac{^{26}c_{13}}{^{52}c_{13}} \)

Question. From a pack of cards, 2 cards are chosen at random. The probability of the event of one card is 10 which is not hearts and another a hearts card is
(a) \( \frac{1}{34} \)
(b) \( \frac{1}{102} \)
(c) \( \frac{8}{663} \)
(d) \( \frac{33}{34} \)
Answer: (a) \( \frac{1}{34} \)

Question. A person draws 2 cards from a well shuffled pack of cards, the cards are replaced after noting their colour. Then another person draws 2 cards after shuffling the pack. The probability that there will be exactly 1 common card is
(a) \( \frac{50}{663} \)
(b) \( \frac{25}{663} \)
(c) \( \frac{100}{663} \)
(d) \( \frac{75}{663} \)
Answer: (a) \( \frac{50}{663} \)

Question. Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is :
(a) \( \frac{1}{2} \)
(b) \( \frac{7}{15} \)
(c) \( \frac{2}{15} \)
(d) \( \frac{1}{3} \)
Answer: (b) \( \frac{7}{15} \)

Question. A box contains 40 balls of the same shape and weight. Among the balls 10 are white, 16 are red and the rest are black, if two balls are drawn, the probability that one is red and one is black is
(a) \( 3/4 \)
(b) \( 56/195 \)
(c) 1
(d) \( 1/4 \)
Answer: (b) \( 56/195 \)

Question. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random wifthout replacement from the urn. The probability that the three balls have different colours is: [AIEEE 2010]
(a) \( \frac{1}{3} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{1}{21} \)
(d) \( \frac{2}{23} \)
Answer: (b) \( \frac{2}{7} \)

Question. If three balls drawn from a bag contains are 4 red, 3 black and 5 white balls. The probability of drawing 2 balls of the same colour and one is of different colour is
(a) \( \frac{5}{44} \)
(b) \( \frac{15}{44} \)
(c) \( \frac{29}{44} \)
(d) \( \frac{131}{195} \)
Answer: (c) \( \frac{29}{44} \)

Question. From a bag containing 4 white and 5 black balls 3 are drawn at random. The odds against these being all black balls is
(a) 5 to 42
(b) 37 to 5
(c) 5 to 37
(d) 42 to 5
Answer: (b) 37 to 5

Question. A box X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is
(a) \( 2/15 \)
(b) \( 7/15 \)
(c) \( 8/15 \)
(d) \( 14/15 \)
Answer: (c) \( 8/15 \)

Question. Box A contains 3 red and 2 black balls. Box B contains 2 red and 3 black balls. One ball is drawn at random from box A and placed in box B. Then one ball is drawn at random from the box B and placed in A. The probability that the composition of balls in the two boxes remains unaltered is
(a) \( \frac{9}{30} \)
(b) \( \frac{4}{15} \)
(c) \( \frac{17}{30} \)
(d) \( \frac{16}{30} \)
Answer: (c) \( \frac{17}{30} \)

Question. Three ‘\( 1 \times 1 \)’ squares of a chess board having \( 8 \times 8 \) squares being chosen at random, the chance that all the three are white is
(a) \( \frac{^{32}c_{3}}{^{64}c_{3}} \)
(b) \( \frac{^{8}c_{3}}{^{64}c_{3}} \)
(c) \( \frac{^{16}c_{3}}{^{64}c_{3}} \)
(d) \( \frac{^{4}c_{3}}{^{64}c_{3}} \)
Answer: (a) \( \frac{^{32}c_{3}}{^{64}c_{3}} \)

Question. Three ‘\( 1 \times 1 \)’ squares of a chess board having \( 8 \times 8 \) squares are chosen at random, the chance that 2 are of one colour and 1 is of different colour is
(a) \( \frac{^{32}c_{3}}{^{64}c_{3}} \)
(b) \( \frac{^{16}c_{3}}{^{64}c_{3}} \)
(c) \( \frac{2 \times ^{32}c_{2} \times ^{32}c_{1}}{^{64}c_{3}} \)
(d) 1
Answer: (c) \( \frac{2 \times ^{32}c_{2} \times ^{32}c_{1}}{^{64}c_{3}} \)

PROBLEMS ON ADDITION THEOREM

Question. If A and B are two events such that \( P(A) = \frac{1}{4} \), \( P(A \cup B) = \frac{1}{3} \) and P(B) = P, the value of P if \( A \subset B \)
(a) \( \frac{1}{12} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{3} \)
Answer: (d) \( \frac{1}{3} \)

Question. Suppose that A and B are two events such that \( P(A \cap B) = \frac{3}{25} \) and \( P(B - A) = \frac{8}{25} \). Then P(B) =
(a) \( \frac{11}{25} \)
(b) \( \frac{3}{11} \)
(c) \( \frac{1}{11} \)
(d) \( \frac{9}{11} \)
Answer: (a) \( \frac{11}{25} \)

Question. Two events A and B have the probabilities 0.25 and 0.5 respectively. The probability that both A and B occur simultaneously is 0.14. The probability that neither A nor B occurs is
(a) 0.39
(b) 0.29
(c) 0.19
(d) 0.5
Answer: (a) 0.39

Question. If A,B and C are mutually exclusive and exhaustive events of a random experiment such that \( P(B) = \frac{3}{2} P(A) \) and \( P(C) = \frac{1}{2} P(B) \) then \( P(A \cup C) = \) 
(a) \( \frac{3}{13} \)
(b) \( \frac{6}{13} \)
(c) \( \frac{7}{13} \)
(d) \( \frac{10}{13} \)
Answer: (a) \( \frac{3}{13} \)

Question. A and B are seeking admission into IIT. If the probability for A to be selected is 0.5 and that of both to be selected is 0.3. The at most probability of B is
(a) 0.9
(b) 0.8
(c) 0.6
(d) 0.4
Answer: (b) 0.8

Question. There are three events A, B and C one of which and only one can happen. The odds are 7 to 3 against A and 6 to 4 against B. The odds against C are
(a) 3 to 4
(b) 4 to 3
(c) 7 to 3
(d) 3 to 7
Answer: (c) 7 to 3