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 $\overline{\left(A\right)}$ = 0.5, find P(B).

Answer 1

Given:
P (A ∪ B) = 0.8, P (A ∩ B) = 0.3 and $P\left(\overline{A}\right)=0.5$
We know that
$P\left(A\right)+P\left(\overline{A}\right)=1$
$\Rightarrow P\left(A\right)+0.5=1$
$\Rightarrow P\left(A\right)=1-0.5=0.5$
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