Question

In a random experiment, let A and B be events such that P(A or B) = 0.7, P(A and B) = 0.3 and P bar (A) = 0.4. Find P(B).

Answer 1

Given : \(P( \bar{A})\) = 0.4, P(A or B) = 0.7 and P(A and B) = 0.3 

To find : P(B) 

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

P(A or B) = P(A) + P(B) - P(A and B) 

We have \(P( \bar{A})\) = 0.4 

P(A) = 1 – 0.4 = 0.6 

We get P(A) = 0.6 

Substituting in the above formula we get, 

0.7 = 0.6 + P(B) – 0.3 

0.7 = 0.3 + P(B) 

0.7 – 0.3 = P(B) 

0.4 = P(B) 

P(B) = 0.4