Question

If $A$ and $B$ are events having probabilities, $P\left(A\right)=0.6,P\left(B\right)=0.4,P(A\cap B)=0$, then the probability that neither $A$ nor $B$ occurs is

• A. $\frac{1}{4}$
• B. $1$
• C. $\frac{1}{2}$
• D. $0$

Answer 1

The correct option is D $0$

P(A u B) $=$ P(A) + P(B) - P(A n B)

P(A u B) $=$ probability that either A or B occurs

P(A n B) $=$ probability that both A & B occur

Plugging the values of P(A), P(B), P(A n B)

we get,

P(A u B) $=0.6+0.4-0$

P(A u B) $=1$

This means, there is $100\%$ chance that either event A or B occurs all the time.

Which means, the probability of neither A nor B occurring will be 0, because one of them will occur $100\%$ of the time.