Question

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of 

(i) P(A ∪ B) 

(ii) P(A ∩ \(\bar{B}\)) 

(iii) P(\(\bar{A}\) ∩ B)

Answer 1

P(A) = 0.5, P(B) = 0.3 

Here A and B are mutually exclusive.

(i) P(A ∪ B) = P(A) + P(B) 

= 0.5 + 0.3 = 0.8 

(ii) P(A ∩ B) = P(A) + P(B) – P(A ∪ B) 

= 0.5 + 0.3 – 0.8

P(A ∩ B) = 0 

P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B) = 0.5 – 0 = 0.5 

(iii) P(\(\bar{A}\) ∩ B) = P(B) – P(A ∩ B) = 0.3 – 0 = 0.3