Question

If P(A)=0.2, P(B)=0.5, and P(A∪B)=0.7, then

P(A∩B)=
.
(a) Are events A and B independent? (enter YES or NO)

(b) Are A and B mutually exclusive? (enter YES or NO)

Answer 1

(a) (NO)

(b) (YES)

Explanation:

We have that:

P(A)=0.2, P(B)=0.5, and P(A∪B)=0.7

To find P(A∩B), we use the relation:

P(A∪B)=P(A)+P(B)- P(A∩B)

We substitute to get:

0.7=0.2+0.5-P(A∩B)

0.7=0.7-P(A∩B)

P(A∩B)=0.7-0.7

P(A∩B)=0

Events A and B are disjoint and hence are mutually exclusive.

P(A∩B)≠P(A)×P(B).

Hence the two events are not independent.