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)

(a) (NO)

(b) (YES)

Step-by-step 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.