Question

The sum of probabilities of two mutually exclusive events will always be 1.

• A. True
• B. False

Answer 1

The correct option is B

False

The sum of probabilities of two mutually exclusive events need not be always 1.
For example, consider the events “getting a prime number”, and “getting a composite number” for the experiment of rolling a die. They are mutually exclusive, but the sum of their probabilities is less than 1.

Favorable outcomes for prime no. = 2 , 3, 5
Favorable outcomes for composite no. = 4, 6
P(getting a prime no.) $=\frac{3}{6}=\frac{1}{2}$
P(getting a composite no.) $=\frac{2}{6}=\frac{1}{3}$

$\frac{1}{2}+\frac{1}{3}\ne 1.$ So The sum of probabilities of two mutually exclusive events need not be always 1.