Question

The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ____________.

Answer 1

Given, P(A) = 0.5
P(B) = 0.3
then P(A∪B) = P(A) + P(B) – P(A∩B)
= 0.5 + 0.3 – 0 (Since A and B are mutually exclusive)
i.e P(A∪B) = 0.8
then $P\left(\overline{A}\cap \overline{B}\right)=1-P\left(A\cup B\right)\left[\therefore \left(\overline{A}\cap \overline{B}\right)=A\cup B\mathrm{By}\mathrm{De}\mathrm{morgan}\text{'}\mathrm{s}\mathrm{law}\right]$
= 1 – 0.8
i.e $P\left(\overline{A}\cup \overline{B}\right)$ = 0.2
Hence, probability of neither A nor B is 0.2