Class 11 Mathematics Probability MCQs Set 07

Question. If A and B are independent events of a random experiment such that \( P(A \cap B) = \frac{1}{6} \) and \( P(\overline{A} \cap \overline{B}) = \frac{1}{3} \) then \( P(A) = \)
(a) 1/4, 1/3
(b) 1/3, 1/2
(c) 1/2, 1/5
(d) 2/3, 1/3
Answer: (b) 1/3, 1/2

Question. A and B are two events such that \( P(A) = 0.4 \), \( P(A \cup B) = 0.7 \). If A and B are independent then P(B) =
(a) 0.3
(b) 0.4
(c) 0.5
(d) 0.7
Answer: (c) 0.5

Question. A problem is given to 3 students. Their chances of solving it individually are \( \frac{1}{3}, \frac{1}{4} \) and \( \frac{1}{5} \). The probability that the problem will be solved is
(a) \( \frac{2}{5} \)
(b) \( \frac{3}{5} \)
(c) \( \frac{4}{5} \)
(d) \( \frac{1}{5} \)
Answer: (b) \( \frac{3}{5} \)

Question. In a shooting test the probability of A,B,C hitting the targets are 1/2 , 2/3 and 3/4 respectively. If all of them fire at the same target. The probability that only one of them hits the target is
(a) \( \frac{1}{5} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{1}{3} \)
(d) \( \frac{1}{4} \)
Answer: (d) \( \frac{1}{4} \)

Question. A person is known to hit the target in 3 out of 4 shots, where as an other person is known to hit twice in every three attempts. If both of them try independently the probability that the target being hit is
(a) \( \frac{1}{12} \)
(b) \( \frac{11}{12} \)
(c) \( \frac{5}{12} \)
(d) \( \frac{3}{12} \)
Answer: (b) \( \frac{11}{12} \)

Question. A speaks truth in 75% of the cases and B in 80% of the cases. The percentage of cases they are likely to concur with each other in making the same statement is
(a) 25%
(b) 35%
(c) 50%
(d) 65%
Answer: (d) 65%

Question. The probability that a student passes in Mathematics is \( \frac{2}{3} \) and the probability that he passes in English is \( \frac{4}{9} \). The probability that he passes in any one of the courses is \( \frac{4}{5} \). The probability that he passes in both is
(a) \( \frac{11}{45} \)
(b) \( \frac{14}{45} \)
(c) \( \frac{17}{45} \)
(d) \( \frac{15}{45} \)
Answer: (b) \( \frac{14}{45} \)

Question. Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is
(a) \( \frac{3}{5} \)
(b) \( \frac{5}{6} \)
(c) \( \frac{1}{36} \)
(d) \( \frac{1}{6} \)
Answer: (a) \( \frac{3}{5} \)

Question. A bag contains 17 counters marked with numbers 1 to 17 on chits. A counter is drawn and replaced. A second draw is then made. The chance that the number on the counter drawn 1st is even and the second is odd is
(a) \( \frac{64}{289} \)
(b) \( \frac{81}{289} \)
(c) \( \frac{72}{289} \)
(d) \( \frac{36}{289} \)
Answer: (c) \( \frac{72}{289} \)

Question. Two cards are selected at random from 10 cards numbered 1 to 10. The probaility that their sum is odd, if the 2 cards are drawn one after an other without replacement is
(a) \( \frac{5}{9} \)
(b) \( \frac{4}{9} \)
(c) \( \frac{2}{9} \)
(d) \( \frac{3}{9} \)
Answer: (a) \( \frac{5}{9} \)

Question. A and B are two events such that P(A)=0.5, \( P(A \cup B) = 0.7 \). If A and B are independent events P(B) =
(a) \( \frac{1}{5} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{3}{5} \)
(d) \( \frac{4}{5} \)
Answer: (c) \( \frac{3}{5} \)

Question. There are 10 cards in a bag. On 5 of them "N" is printed and on the other 5 "C" is printed. 3 cards are drawn, one after an other without replacement and kept in that order. The probability that the word formed with the letters is NCC is
(a) \( \frac{5}{36} \)
(b) \( \frac{7}{36} \)
(c) \( \frac{11}{36} \)
(d) \( \frac{3}{36} \)
Answer: (a) \( \frac{5}{36} \)

Question. For an oral test 25 questions are set of which 5 are easy and 20 are tough. Two questions are given to two candidates A and B in that order (one question to each person). The probability for B to receive easy question is
(a) \( \frac{1}{5} \)
(b) \( \frac{4}{5} \)
(c) \( \frac{5}{24} \)
(d) \( \frac{19}{24} \)
Answer: (a) \( \frac{1}{5} \)

Question. Three faces of a fair die are yellow, two faces red and one blue. The die is tossed 3 times. The probability that the colours yellow, red and blue appear in the 1st, 2nd and 3rd tosses respectively is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{35}{36} \)
(d) \( \frac{1}{3} \)
Answer: (b) \( \frac{1}{36} \)

Question. The chance of throwing an ace in the 1st only, of the two successive throws with an ordinary die is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{5}{36} \)
(d) \( \frac{5}{6} \)
Answer: (c) \( \frac{5}{36} \)

Question. From a well shuffled pack of 52 playing cards two cards are drawn at random, one after an other without replacement. The probability that 1st one is a king and second one is queen is
(a) \( \frac{5}{663} \)
(b) \( \frac{4}{663} \)
(c) \( \frac{1}{221} \)
(d) \( \frac{3}{221} \)
Answer: (b) \( \frac{4}{663} \)

Question. A bag contains 10 white and 8 black balls. Two successive drawings of 2 balls are made. The probability that the 1st draw will give 2 white and the 2nd draw will give 2 black if the drawing is without replacement is
(a) \( \frac{^{10}C_{2} + ^{8}C_{2}}{^{18}C_{2}} \)
(b) \( \frac{^{10}C_{2}}{^{18}C_{2}} \times \frac{^{8}C_{2}}{^{16}C_{2}} \)
(c) \( \frac{^{10}C_{2}}{^{18}C_{2}} \times \frac{^{8}C_{2}}{^{18}C_{2}} \)
(d) \( \frac{^{12}C_{2}}{^{18}C_{2}} \times \frac{^{6}C_{2}}{^{18}C_{2}} \)
Answer: (b) \( \frac{^{10}C_{2}}{^{18}C_{2}} \times \frac{^{8}C_{2}}{^{16}C_{2}} \)

Question. A and B toss a coin alternately till one of them gets a head and wins the game. The probability of A's winning if A starts the game is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{4} \)
Answer: (c) \( \frac{2}{3} \)

Question. A bag contains 4 white and 2 black balls. Another contains 3 white and 5 black balls. If one ball is drawn from each, the probability that both are black is
(a) \( \frac{13}{24} \)
(b) \( \frac{5}{24} \)
(c) \( \frac{1}{14} \)
(d) \( \frac{2}{14} \)
Answer: (b) \( \frac{5}{24} \)

Question. If A and B are two Mutually Exclusive events in a sample space S such that P(B) = 2 P(A) and \( A \cup B = S \) then P(A)=
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{1}{5} \)
Answer: (b) \( \frac{1}{3} \)

Question. From the set of numbers {1, 2, 3, 4, 5, 6, 7, 8} two numbers are selected at random without replacement. The probability that their sum is more than 13 is
(a) \( \frac{1}{14} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{3}{7} \)
(d) \( \frac{4}{7} \)
Answer: (a) \( \frac{1}{14} \)

Question. In a room there are 6 couples. Out of them if 4 are selected at random, the probability that they may be couples is
(a) \( \frac{4}{33} \)
(b) \( \frac{2}{33} \)
(c) \( \frac{1}{33} \)
(d) \( \frac{3}{33} \)
Answer: (c) \( \frac{1}{33} \)

Question. Two letters are taken at random from the word HOME. The probability that at least one is a vowel is
(a) \( \frac{1}{2} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{5}{6} \)
(d) \( \frac{1}{4} \)
Answer: (c) \( \frac{5}{6} \)

Question. Three electric lamps are to be fitted in a room. Three bulbs are chosen at random from 10 bulbs having 6 good bulbs and fitted. The chance that the room is lighted is
(a) \( \frac{1}{30} \)
(b) \( \frac{2}{30} \)
(c) \( \frac{28}{30} \)
(d) \( \frac{29}{30} \)
Answer: (d) \( \frac{29}{30} \)

Question. 5 persons entered the lift cabin on the ground floor of an eight floor house. Suppose each of them independently leave the cabin at any floor beginning with 1st floor, the probability of all the 5 persons leaving at different floor is
(a) \( \frac{^{8}P_{5}}{8^{5}} \)
(b) \( \frac{^{7}P_{5}}{7^{5}} \)
(c) \( \frac{5}{8} \)
(d) \( \frac{1}{8} \)
Answer: (b) \( \frac{^{7}P_{5}}{7^{5}} \)

Question. Four numbers are chosen at random from \( \{1, 2, 3, ......, 40\} \). The probability that they are not consecutive is
(a) \( \frac{1}{2470} \)
(b) \( \frac{4}{7969} \)
(c) \( \frac{2469}{2470} \)
(d) \( \frac{7965}{7969} \)
Answer: (c) \( \frac{2469}{2470} \)

Question. Two numbers are chosen at random from {1, 2, 3, 4, 5, 6, 7, 8} at a time. The probability that smaller of the two numbers is less than 4 is
(a) \( \frac{7}{14} \)
(b) \( \frac{8}{14} \)
(c) \( \frac{9}{14} \)
(d) \( \frac{10}{14} \)
Answer: (c) \( \frac{9}{14} \)

Question. Two numbers are selected at random from 1, 2, 3, ...... 100 without replacement. The probability that the minimum of the two numbers is less than 70 is
(a) \( \frac{^{30}C_{2}}{^{100}C_{2}} \)
(b) \( 1 - \frac{^{30}C_{2}}{^{100}C_{2}} \)
(c) \( \frac{^{31}C_{2}}{^{100}C_{2}} \)
(d) \( 1 - \frac{^{31}C_{2}}{^{100}C_{2}} \)
Answer: (d) \( 1 - \frac{^{31}C_{2}}{^{100}C_{2}} \)

Question. Two symmetrical dice are thrown at a time. If the sum of points on them is 7, the chance that one of them will show a face with 2 points is
(a) \( \frac{1}{8} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{2}{8} \)
Answer: (b) \( \frac{1}{3} \)

Question. Three students A, B and C are to take part in a swimming competition. The probability of A's winning or B's winning each is 3 times the probability of C's winning. The probability of C's winning if there is no tie is
(a) \( \frac{4}{7} \)
(b) \( \frac{3}{7} \)
(c) \( \frac{2}{7} \)
(d) \( \frac{1}{7} \)
Answer: (d) \( \frac{1}{7} \)

Question. Let A be a set of 4 elements. From the set of all functions from A to A, the probability that it is an into function is
(a) \( \frac{3}{32} \)
(b) 0
(c) \( \frac{29}{32} \)
(d) 1
Answer: (c) \( \frac{29}{32} \)

Question. S = {1, 2, 3, .... 20} if 3 numbers are chosen at random from S, the probability for they are in A.P. is
(a) \( \frac{3}{38} \)
(b) \( \frac{35}{33} \)
(c) \( \frac{33}{35} \)
(d) \( \frac{1}{38} \)
Answer: (a) \( \frac{3}{38} \)

Question. The probability of choosing randomly a number c form the set {1, 2, 3, .......9} such that the quadratic equation \( x^{2} + 4x + c = 0 \) has real roots is :
(a) \( \frac{1}{9} \)
(b) \( \frac{2}{9} \)
(c) \( \frac{3}{9} \)
(d) \( \frac{4}{9} \)
Answer: (d) \( \frac{4}{9} \)

Question. A class has fifteen boys and five girls. Suppose three students are selected at random form the class. The probability that there are two boys and one girl is :
(a) \( \frac{35}{76} \)
(b) \( \frac{35}{38} \)
(c) \( \frac{7}{76} \)
(d) \( \frac{35}{72} \)
Answer: (a) \( \frac{35}{76} \)

Question. The probability of getting at least one head when we toss 3 unbiased coins is
(a) \( \frac{3}{8} \)
(b) \( \frac{5}{8} \)
(c) \( \frac{7}{8} \)
(d) \( \frac{1}{8} \)
Answer: (c) \( \frac{7}{8} \)

Question. A tosses 2 coines while B tosses 3. The probability that B obtains more number of heads is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{3}{4} \)
Answer: (c) \( \frac{1}{2} \)

Question. The probability of getting at least 2 heads, when an unbiased coin is tossed 6 times is
(a) \( \frac{63}{64} \)
(b) \( \frac{57}{64} \)
(c) \( \frac{7}{64} \)
(d) \( \frac{37}{64} \)
Answer: (b) \( \frac{57}{64} \)

Question. A fair coin is tossed 4 times. The probability that heads exceed tails in number is
(a) \( \frac{3}{16} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{5}{16} \)
(d) \( \frac{7}{16} \)
Answer: (c) \( \frac{5}{16} \)

Question. An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the prob. of getting a total of odd no. of points is
(a) \( 1/2 \)
(b) \( 1/4 \)
(c) \( 1/8 \)
(d) \( 3/8 \)
Answer: (a) \( 1/2 \)

Question. Two symmetrical dice are thrown. The probability of getting a sum of 6 points is
(a) \( \frac{4}{36} \)
(b) \( \frac{5}{36} \)
(c) \( \frac{6}{36} \)
(d) \( \frac{1}{36} \)
Answer: (b) \( \frac{5}{36} \)