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).
Given : A and B are mutually exclusive events
P(not A) = P() = 0.65 , P(A or B) = 0.65
To find : P(B)
Formula used : P(A) = 1 – P()
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