Class 11 Probability Exemplar 14 1 Exemplar Solutions

Q1

If $P(A) = 0.4$, $P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(A \cup B)$ is

(a) $0.24$
(b) $0.96$
(c) $0.84$
(d) $0.48$

Q2

If $A$ and $B$ are mutually exclusive events, then $P(A \cap B)$ is equal to

(a) $1$
(b) $P(A)P(B)$
(c) $0$
(d) $P(A) + P(B)$

Q3

If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$, and $A$ and $B$ are mutually exclusive events, then $P(A \text{ or } B)$ is

(a) $\frac{4}{5}$
(b) $\frac{2}{5}$
(c) $\frac{3}{25}$
(d) $\frac{1}{5}$

Q4

Two dice are thrown simultaneously. The probability of getting a doublet of even numbers is

(a) $\frac{1}{6}$
(b) $\frac{1}{12}$
(c) $\frac{1}{36}$
(d) $\frac{5}{36}$

Q5

If an event cannot occur, then its probability is

(a) $1$
(b) $\frac{3}{4}$
(c) $\frac{1}{2}$
(d) $0$

Q6

If $P(A) = 0.5$, $P(B) = 0.3$, and $A$ and $B$ are mutually exclusive, then $P(\text{neither } A \text{ nor } B)$ is

(a) $0.8$
(b) $0.2$
(c) $0.15$
(d) $0.5$

Q7

A card is drawn from a well-shuffled pack of $52$ playing cards. The probability that it is a spade or an ace is

(a) $\frac{4}{13}$
(b) $\frac{17}{52}$
(c) $\frac{1}{13}$
(d) $\frac{16}{52}$

Q8

Three coins are tossed once. The probability of getting at least two heads is

(a) $\frac{1}{8}$
(b) $\frac{3}{8}$
(c) $\frac{1}{2}$
(d) $\frac{5}{8}$

Q9

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$, $P(B) = \frac{1}{2}$ and $P(A \cap B) = \frac{1}{8}$, then $P(\text{not } A \text{ and not } B)$ is

(a) $\frac{3}{8}$
(b) $\frac{5}{8}$
(c) $\frac{1}{8}$
(d) $\frac{7}{8}$

Q10

The odds in favour of an event are $3 : 5$. The probability of occurrence of the event is

(a) $\frac{3}{5}$
(b) $\frac{5}{3}$
(c) $\frac{3}{8}$
(d) $\frac{5}{8}$

Q11

A letter is chosen at random from the word 'ASSASSINATION'. The probability that the letter is a vowel is

(a) $\frac{6}{13}$
(b) $\frac{7}{13}$
(c) $\frac{5}{13}$
(d) $\frac{4}{13}$

Q12

If $E$ and $F$ are events such that $P(E) \le P(F)$ and $P(E \cap F) > 0$, then which of the following is always true?

(a) $E \subset F$
(b) Occurrence of $E \implies$ occurrence of $F$
(c) $P(E \cap F) \le P(E)$
(d) none of these

Q13

If $P(A \cup B) = P(A \cap B)$ for two events $A$ and $B$, then

(a) $P(A) = P(B)$
(b) $P(A) + P(B) = 1$
(c) $P(A) = 0$
(d) none of these

Q14

In a non-leap year, the probability of having $53$ Sundays is

(a) $\frac{1}{7}$
(b) $\frac{2}{7}$
(c) $\frac{5}{7}$
(d) $\frac{3}{7}$

Q15

If $A$ and $B$ are two mutually exclusive and exhaustive events, and $P(A) = 2P(B)$, then $P(A)$ is equal to

(a) $\frac{1}{3}$
(b) $\frac{2}{3}$
(c) $\frac{1}{2}$
(d) $\frac{3}{4}$

Chapter 14 - Probability

Overview

Objective Type Questions (MCQs)