CBSE Class 12 Mathematics Probability Important Questions Set 01

Multiple Choice Questions

Question. From the set {1, 2, 3, 4, 5}, two numbers a and b (\( a \neq b \)) are chosen at random. The probability that \( \frac{a}{b} \) is an integer is
(a) \( \frac{1}{3} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{3}{5} \)
Answer: (b)

Question. A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random (without replacement), then the probability that both the balls are white is  
(a) \( \frac{1}{18} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{1}{12} \)
(d) \( \frac{1}{24} \)
Answer: (c)

Question. A and B are events such that \( P(A) = 0.4, P(B) = 0.3 \) and \( P(A \cup B) = 0.5 \). Then \( P(B' \cap A) \) equals  
(a) \( \frac{2}{3} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{3}{10} \)
(d) \( \frac{1}{5} \)
Answer: (d)

Question. You are given that A and B are two events such that \( P(B) = \frac{3}{5}, P(A | B) = \frac{1}{2} \) and \( P(A \cup B) = \frac{4}{5} \), then \( P(A) \) equals
(a) \( \frac{3}{10} \)
(b) \( \frac{1}{5} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{3}{5} \)
Answer: (c)

Question. Three persons, A, B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is
(a) 0.024
(b) 0.188
(c) 0.336
(d) 0.452
Answer: (b)

Question. Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is 
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{4}{7} \)
Answer: (d)

Question. A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{8} \)
(d) \( \frac{3}{4} \)
Answer: (c)

Question. A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is
(a) \( \frac{3}{28} \)
(b) \( \frac{2}{21} \)
(c) \( \frac{1}{28} \)
(d) \( \frac{167}{168} \)
Answer: (a)

Question. A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is
(a) \( \frac{33}{56} \)
(b) \( \frac{9}{64} \)
(c) \( \frac{1}{14} \)
(d) \( \frac{3}{28} \)
Answer: (d)

Question. Two dice are thrown. If it is known that the sum of number on the dice was less than 6, the probability of getting a sum 3, is
(a) \( \frac{1}{18} \)
(b) \( \frac{5}{18} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{2}{5} \)
Answer: (c)

Question. Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is
(a) \( \frac{1}{13} \times \frac{1}{13} \)
(b) \( \frac{1}{13} \times \frac{1}{12} \)
(c) \( \frac{1}{13} \times \frac{1}{17} \)
(d) \( \frac{1}{13} \times \frac{4}{51} \)
Answer: (a)

Question. A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is
(a) \( \frac{15}{196} \)
(b) \( \frac{131}{392} \)
(c) \( \frac{15}{56} \)
(d) \( \frac{15}{29} \)
Answer: (c)

Question. Three persons A, B and C, fire at a target in turn, standing with A. Their probability of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is
(a) 0.025
(b) 0.188
(c) 0.339
(d) 0.475
Answer: (b)

Question. The probability distribution of a discrete random variable X is given below:

The value of k is
(a) 8
(b) 16
(c) 32
(d) 48
Answer: (c)

Question. Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’, then \( P(A \cap B) \) is
(a) \( \frac{1}{36} \)
(b) \( \frac{7}{4} \)
(c) \( \frac{9}{20} \)
(d) None of these
Answer: (a)

Question. In a college, 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is
(a) \( \frac{1}{10} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{9}{20} \)
(d) \( \frac{1}{3} \)
Answer: (b)

Question. A and B are two students. Their chances of solving a problem correctly are \( \frac{1}{3} \) and \( \frac{1}{4} \), respectively. If the probability of their making a common error is \( \frac{1}{20} \) and they obtain the same answer, then the probability of their answer to be correct is
(a) \( \frac{1}{12} \)
(b) \( \frac{1}{40} \)
(c) \( \frac{13}{120} \)
(d) \( \frac{10}{13} \)
Answer: (d)

Question. Let X be a discrete random variable assuming values \( x_1, x_2, \dots, x_n \) with probabilities \( p_1, p_2, \dots, p_n \), respectively. Then variance of X is given by  
(a) \( E(X^2) \)
(b) \( E(X^2) + E(X) \)
(c) \( E(X^2) - [E(X)]^2 \)
(d) \( \sqrt{E(X^2) - [E(X)]^2} \)
Answer: (c)

Question. The probability that a student is not a swimmer is \( \frac{1}{5} \). Then the probability that out of five students, four are swimmers is
(a) \( {}^5C_4 \left( \frac{4}{5} \right)^4 \left( \frac{1}{5} \right) \)
(b) \( \left( \frac{4}{5} \right)^4 \cdot \frac{1}{5} \)
(c) \( {}^5C_1 \left( \frac{4}{5} \right) \left( \frac{1}{5} \right)^4 \)
(d) None of these
Answer: (a)

Question. Which one of the following is not a requirement of a binomial distribution?
(a) There are two outcomes for each trial
(b) There is a fixed number of trials
(c) The outcomes must be dependent on each other.
(d) The probability of success must be the same for all trials.
Answer: (c)