Question

Let A and B be two mutually exclusive events of a random experiment such that P(not A) = 0.65 and P(A or B) = 0.65, find P(B).

Answer 1

Given : A and B are mutually exclusive events 

P(not A) = P\(\overline{A}\) = 0.65 , P(A or B) = 0.65 

To find : P(B) 

Formula used : P(A) = 1 – P(\(\overline{A}\))

P(A or B) = P(A) + P(B) - P(A and B)

For mutually exclusive events A and B, P(A and B) = 0

P(A) = 1 – P(not A)

P(A) = 1 – 0.65

P(A) = 0.35 

Substituting in the above formula we get, 

0.65 = 0.35 + P(B)

P(B) = 0.65 – 0.35

P(B) = 0.30

P(B) = 0.30