Question

If A and B are two events, then the probability of occurrence of exactly one of A and B is _____________.

Answer 1

for two events A and B Probability of occurrence of exactly are of A and B is $P\left(\overline{A}\cap B\right)+P\left(A\cap \overline{B}\right)$
= P(B) – P(A∩B) + P(A) – P(A∩B)
= P(A) + P(B) – 2 P(A∩B)
i.e probability of occurrence of exactly are of A and B is P(A) + P(B) – 2 P(A∩B)