Question

If A and B are two events associated with a random experiment such that
P (A ∪ B) = 0.8, P (A ∩ B) = 0.3 and P \[(\bar{A} )\]= 0.5, find P(B).

 

Answer 1

Given:
P (A ∪ B) = 0.8, P (A ∩ B) = 0.3 and 

\[P\left( \bar{A} \right) = 0 . 5\]

We know that

\[P\left( A \right) + P\left( \bar{A} \right) = 1\]

\[\Rightarrow P\left( A \right) + 0 . 5 = 1\]

\[\Rightarrow P\left( A \right) = 1 - 0 . 5 = 0 . 5\]

By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
⇒ 0.8 = 0.5 + P (B) - 0.3
⇒ 0.8 = 0.2 + P (B)
⇒ P (B) = 0.8 

0.2
              = 0.6
Hence, P (B) = 0.6