Question

The probability of occurrence of an event A is 0.3 and that of occurrence of an event B is 0.4. If A and B are mutually exclusive, then the probability that neither A occurs nor B occurs is:

• A. 0.2
• B. 0.35
• C. 0.3
• D. none of these

Answer 1

Answer: (C)

Given: P(A) = 0.3, P(B) = 0.4, A and B are mutually exclusive
$\therefore P(A\cap B)=0$
we know that
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$\Rightarrow P(A\cup B)=0.3+0.4-0=0.7$
The probability that neither A occurs nor B
occurs $=P\overline{(A\cup B)}$
$\therefore P(\overline{A\cup B})=1-P(A\cup B)$
$=1-0.7=0.3$