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 $