Answer to Question #282347 in Statistics and Probability for Bismark Akyen

Question

(b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5;

i. Find P(A n B) and P(AUB)

ii. Are A and B mutually exclusive? Explain.

Answer 1

i.

$$P(A\cap B)=P(A)P(B)=0.3(0.5)=0.15$$

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

$$=0.3+0.5-0.15=0.65$$

ii.

$$P(A\cup B)=0.65\not=0.3+0.5=P(A)+P(B)$$

A and B are not mutually exclusive.