Question

Two events, A and B, are disjoint. What is the probability that both A and B will occur at the same time?

Answer 1

ANSWER

$P(A\cap B)=0$

EXPLANATION

If the two events are disjoint, then they are mutually exclusive.

This means that their intersection is zero.

Therefore

$n(A\cap B)=0$

This implies that,

$P(A\cap B)= \frac{n(A\cap B)}{n(U)}$

$P(A\cap B)= \frac{0}{n(U)} = 0$

The probability that the two events will occur together is 0, which means an impossibility.