Class 11 Mathematics Probability MCQs Set 06

Question. Two symmetrical dice are thrown at a time. The probability that they show different faces is
(a) \( \frac{5}{6} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{25}{36} \)
(d) \( \frac{1}{18} \)
Answer: (a) \( \frac{5}{6} \)

Question. Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is
(a) \( \frac{1}{4} \)
(b) \( \frac{5}{36} \)
(c) \( \frac{5}{12} \)
(d) \( \frac{5}{6} \)
Answer: (c) \( \frac{5}{12} \)

Question. When two dice are thrown, the probability of getting equal numbers is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{1}{3} \)
Answer: (a) \( \frac{1}{6} \)

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

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

Question. The probability that a non-leap year will have only 52 Fridays is
(a) \( \frac{3}{7} \)
(b) \( \frac{4}{7} \)
(c) \( \frac{5}{7} \)
(d) \( \frac{6}{7} \)
Answer: (d) \( \frac{6}{7} \)

Question. The chance that a leap year selected at random will contain 53 sundays is
(a) 1/7
(b) 1/14
(c) 2/7
(d) 4/7
Answer: (b) 1/14

Question. Two cards are drawn at random from a pack of 52 well shuffled playing cards. The probability that the cards drawn are aces is
(a) \( \frac{5}{221} \)
(b) \( \frac{3}{221} \)
(c) \( \frac{1}{221} \)
(d) \( \frac{4}{221} \)
Answer: (c) \( \frac{1}{221} \)

Question. When a card is drawn at random from a well shuffled pack of 52 playing cards, the probability that it may be either king or queen is
(a) \( \frac{8}{13} \)
(b) \( \frac{5}{13} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{1}{13} \)
Answer: (c) \( \frac{2}{13} \)

Question. If two cards are drawn from a well shuffled pack of 52 playing cards, the probability that there will be at least one club card is
(a) \( \frac{^{39}C_{2}}{^{52}C_{2}} \)
(b) \( 1 - \frac{^{39}C_{2}}{^{52}C_{2}} \)
(c) \( \frac{39}{52} \times \frac{39}{52} = \frac{9}{16} \)
(d) \( \frac{^{30}C_{2}}{^{52}C_{2}} \)
Answer: (b) \( 1 - \frac{^{39}C_{2}}{^{52}C_{2}} \)

Question. From a well shuffled pack of 52 playing cards two cards are drawn at random. The probability that either both are red or both are kings is
(a) \( \frac{(^{26}C_{2} + ^{4}C_{2})}{^{52}C_{2}} \)
(b) \( \frac{(^{26}C_{2} + ^{4}C_{2} - ^{2}C_{2})}{^{52}C_{2}} \)
(c) \( \frac{^{30}C_{2}}{^{52}C_{2}} \)
(d) \( \frac{^{39}C_{2}}{^{52}C_{2}} \)
Answer: (b) \( \frac{(^{26}C_{2} + ^{4}C_{2} - ^{2}C_{2})}{^{52}C_{2}} \)

Question. From a well shuffled pack of 52 playing cards, four are drawn at random. The probability that all are spades, but one is a king is
(a) \( \frac{^{39}C_{4}}{^{52}C_{4}} \)
(b) \( \frac{^{12}C_{3}}{^{52}C_{4}} \)
(c) \( 1 - \frac{^{39}C_{4}}{^{52}C_{4}} \)
(d) \( \frac{^{12}C_{4}}{^{52}C_{4}} \)
Answer: (b) \( \frac{^{12}C_{3}}{^{52}C_{4}} \)

Question. Two cards are drawn from a well shuffled pack of 52 playing cards. The probability that they belong to different colours is
(a) \( \frac{2 \times ^{13}C_{2}}{^{52}C_{2}} \)
(b) \( \frac{^{4}C_{2} \times 13 \times 13}{^{52}C_{2}} \)
(c) \( \frac{^{26}C_{1} \times ^{26}C_{1}}{^{52}C_{2}} \)
(d) \( \frac{^{13}C_{2}}{^{52}C_{2}} \)
Answer: (c) \( \frac{^{26}C_{1} \times ^{26}C_{1}}{^{52}C_{2}} \)

Question. A card is drawn from a well shuffled pack of 52 cards numbered 2 to 54 The probability that the number on the card is a prime less than 10 is
(a) \( \frac{4}{13} \)
(b) \( \frac{3}{13} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{1}{13} \)
Answer: (d) \( \frac{1}{13} \)

Question. Two cards are drawn from a well shuffled pack of 52 playing cards. The probability that one is a heart card and the other is not a heart card is
(a) \( \frac{7}{34} \)
(b) \( \frac{9}{34} \)
(c) \( \frac{13}{34} \)
(d) \( \frac{15}{34} \)
Answer: (c) \( \frac{13}{34} \)

Question. A card is drawn at random from a well shuffled pack of 52 cards. Again a card is drawn at random from the remaining cards. The probability that one is a king and the other is a queen is
(a) \( \frac{4}{663} \)
(b) \( \frac{8}{663} \)
(c) \( \frac{1}{221} \)
(d) \( \frac{2}{663} \)
Answer: (b) \( \frac{8}{663} \)

Question. The probability of drawing a card which is at least a spade or a king from a well shuffled pack of cards is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{13} \)
(c) \( \frac{4}{13} \)
(d) \( \frac{2}{13} \)
Answer: (c) \( \frac{4}{13} \)

Question. An urn contains 25 balls numbered 1 to 25. Two balls drawn one at a time with replacement. The probability that both the numbers on the balls are odd is
(a) \( \frac{^{13}C_{2}}{625} \)
(b) \( \frac{169}{625} \)
(c) \( \frac{^{25}C_{2}}{625} \)
(d) \( \frac{139}{625} \)
Answer: (b) \( \frac{169}{625} \)

Question. A bag contains 10 balls out of which two are red, three are blue and five are black. Three balls are drawn at random from the bag. The probability that the balls are of the same colour is
(a) \( \frac{9}{120} \)
(b) \( \frac{11}{120} \)
(c) \( \frac{13}{120} \)
(d) \( \frac{17}{120} \)
Answer: (b) \( \frac{11}{120} \)

Question. 3 red and 4 white balls of different sizes are arranged in a row at random. The probability that no two balls of the same colour are together is
(a) \( \frac{6}{35} \)
(b) \( \frac{3}{35} \)
(c) \( \frac{1}{35} \)
(d) \( \frac{9}{35} \)
Answer: (c) \( \frac{1}{35} \)

Question. A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same color is
(a) 1/15
(b) 2/5
(c) 4/15
(d) 7/15
Answer: (d) 7/15

Question. Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is
(a) \( \frac{7}{^{11}C_{7}} \)
(b) \( \frac{^{5}C_{3} + ^{6}C_{4}}{^{11}C_{7}} \)
(c) \( \frac{^{5}C_{3} \times ^{6}C_{4}}{^{11}C_{7}} \)
(d) \( \frac{^{6}C_{3} \times ^{5}C_{4}}{^{11}C_{7}} \)
Answer: (c) \( \frac{^{5}C_{3} \times ^{6}C_{4}}{^{11}C_{7}} \)

Question. If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls, then the probability that the drawn balls are of different colours is
(a) \( \frac{60}{66} \)
(b) \( \frac{47}{66} \)
(c) \( \frac{12}{60} \)
(d) \( \frac{13}{60} \)
Answer: (b) \( \frac{47}{66} \)

Question. A bag contains 3 red, 4 white and 7 black balls. The probability of drawing a red or a black ball is
(a) \( \frac{2}{7} \)
(b) \( \frac{5}{7} \)
(c) \( \frac{3}{7} \)
(d) \( \frac{4}{7} \)
Answer: (b) \( \frac{5}{7} \)

Question. Three '\( 1 \times 1 \)' squares of a chess board having \( 8 \times 8 \) squares are chosen at random, the chance that all the three of the same colour is
(a) \( \frac{^{32}C_{3}}{^{64}C_{3}} \)
(b) \( \frac{2 \times ^{32}C_{3}}{^{64}C_{3}} \)
(c) 1
(d) \( \frac{^{4}C_{3}}{^{64}C_{3}} \)
Answer: (b) \( \frac{2 \times ^{32}C_{3}}{^{64}C_{3}} \)

Question. If A and B are events of a random experiment such that \( P(A \cup B) = 4/5 \), \( P(\overline{A} \cup \overline{B}) = 7/10 \), \( P(B) = 2/5 \), then P(A) =
(a) \( \frac{9}{10} \)
(b) \( \frac{8}{10} \)
(c) \( \frac{7}{10} \)
(d) \( \frac{3}{5} \)
Answer: (c) \( \frac{7}{10} \)

Question. If A and B are two events such that \( P(A \cup B) = \frac{3}{4} \), \( P(A \cap B) = \frac{1}{4} \) & \( P(\overline{A}) = \frac{2}{3} \), then \( P(\overline{A} \cap B) = \)
(a) \( \frac{1}{12} \)
(b) \( \frac{2}{12} \)
(c) \( \frac{7}{12} \)
(d) \( \frac{5}{12} \)
Answer: (d) \( \frac{5}{12} \)

Question. In a swimming competition, only 3 students A, B and C are taking part. The probability of A's winning or the probability of B's winning is three times the probability of C's winning. The probability of the event either B or C to win is
(a) \( \frac{1}{7} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{3}{7} \)
(d) \( \frac{4}{7} \)
Answer: (d) \( \frac{4}{7} \)

Question. Two events A and B have probability 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is
(a) 0.39
(b) 0.25
(c) 0.89
(d) 0.50
Answer: (a) 0.39

Question. In a class of 60 boys and 20 girls, half of the boys and half of the girls know cricket, then the probability of the event that a person selected from the class is either a boy, or a girl who knows cricket is
(a) \( \frac{1}{2} \)
(b) \( \frac{3}{8} \)
(c) \( \frac{5}{8} \)
(d) \( \frac{7}{8} \)
Answer: (d) \( \frac{7}{8} \)

Question. In a class of 125 students, 70 passed in mathematics, 55 passed in statistics and 30 in both. The probability that a student selected at random from that class has passed in only one subject
(a) \( \frac{13}{25} \)
(b) \( \frac{3}{25} \)
(c) \( \frac{17}{25} \)
(d) \( \frac{8}{25} \)
Answer: (a) \( \frac{13}{25} \)

Question. The probability that a company executive will travel by train is 2/3 and that he will travel by plane is 1/5. The probability of his travelling by train or plane is
(a) \( \frac{2}{15} \)
(b) \( \frac{13}{15} \)
(c) \( \frac{15}{13} \)
(d) \( \frac{15}{2} \)
Answer: (b) \( \frac{13}{15} \)

Question. There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. The probability that it may be either green or black is
(a) \( \frac{5}{18} \)
(b) \( \frac{6}{18} \)
(c) \( \frac{11}{18} \)
(d) \( \frac{13}{18} \)
Answer: (c) \( \frac{11}{18} \)

Question. A bag contains 25 balls numbered 1 to 25. One ball is drawn at random. The probability that the number on the ball drawn will be a multiple of 5 or 6 is
(a) \( \frac{3}{25} \)
(b) \( \frac{7}{25} \)
(c) \( \frac{9}{25} \)
(d) \( \frac{5}{25} \)
Answer: (c) \( \frac{9}{25} \)

Question. Suppose there are 12 boys and 4 girls in a class. If we choose three children one after another in succession at random, the probability that all the three are boys is
(a) \( \frac{5}{28} \)
(b) \( \frac{11}{28} \)
(c) \( \frac{9}{28} \)
(d) \( \frac{3}{4} \)
Answer: (b) \( \frac{11}{28} \)

Question. A perfect die is rolled. If the outcome is an odd number, the probability that it is a prime is
(a) \( \frac{1}{3} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{8} \)
Answer: (b) \( \frac{2}{3} \)

Question. Two dice are thrown at a time and the sum of the numbers on them is 6. The probability of getting the number 4 on any one of them is
(a) \( \frac{2}{5} \)
(b) \( \frac{1}{5} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{3} \)
Answer: (a) \( \frac{2}{5} \)

Question. A die is thrown 3 times. The probability of the event of getting sum of the numbers thrown as 15 when it is known that the first throw was a five is
(a) \( \frac{1}{36} \)
(b) \( \frac{2}{36} \)
(c) \( \frac{3}{36} \)
(d) \( \frac{4}{36} \)
Answer: (c) \( \frac{3}{36} \)

Question. An urn contains 12 red balls and 12 green balls. Suppose two balls are drawn one after another without replacement, then the probability that the second ball drawn is green given that the first ball drawn is red is
(a) \( \frac{6}{23} \)
(b) \( \frac{12}{23} \)
(c) \( \frac{11}{23} \)
(d) \( \frac{17}{23} \)
Answer: (b) \( \frac{12}{23} \)

Question. If A and B are two events such that \( P(A) = \frac{1}{4} \) and \( P(A \cup B) = \frac{1}{3} \) and P(B)=P, the value of P if A and B are independent
(a) \( \frac{1}{9} \)
(b) \( \frac{2}{9} \)
(c) \( \frac{4}{9} \)
(d) \( \frac{5}{9} \)
Answer: (a) \( \frac{1}{9} \)