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)

0.3

Answer 2

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 $= P \overline{(A \cup B)}$ $\therefore \, \, P (\overline{A \cup B}) = 1 - P(A \cup B)$ $= 1 - 0.7 = 0.3$