Let A and B be two events such that the probability that exactly one of them occurs is [2 …

Question

Let A and B be two events such that the
probability that exactly one of them occurs is $${2 \over 5}$$ and the probability that A or B occurs is $${1 \over 2}$$ ,
then the probability of both of them occur
together is :

Accepted Answer

Probability that exactly one of them occurs

P(A) + P(B) -- 2P (A $$ \cap $$ B) = $${2 \over 5}$$ .....(1)

Probability
that A or B occurs is

P(A) + P(B) -- P(A $$ \cap $$ B) = $${1 \over 2}$$ ......(2)

Doing (2) - (1)

P(A $$ \cap $$ B) = $${1 \over 2} - {2 \over 5}$$ = 0.10

Solutions · 1