Question

If A and B are any two events, then the probability that exactly one of them occur, is

• A. $P(A\cap \overline{B})+P(\overline{A}\cap B)$
• B. $P(A\cup \overline{B})+P(\overline{A}\cup B)$
• C. $P\left(A\right)+P\left(B\right)-P(A\cap B)$
• D. $P\left(A\right)+P\left(B\right)+2P(A\cap B)$

Answer 1

The correct option is A $P(A\cap \overline{B})+P(\overline{A}\cap B)$

Probability that exactly one of them occurs
= P{(A occur B not occur)or(B occur A not occur)}
$=P(A\cap \overline{B})+P(\overline{A}\cap B)$