Question

If A and B are two events associated with a random experiment such that $P(A\cup B)=0.8,P(A\cap B)=0.3$ and $P\left(\overline{A}\right)=0.5$, find P(B).

Answer 1

We know,

$P(A\cup B)=0.8$

$P(A\cap B)=0.3$

$\Rightarrow P\left(\overline{A}\right)+P\left(A\right)=0.5$

$\Rightarrow P\left(A\right)=1-0.5=0.5$

Now, by addition theorem on probability

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

0.8 = 0.5+ P(B) - 0.3

0.8 = P(B) + 0.2

P(B) = 0.8 -0.2 = 0.6

$\therefore P\left(B\right)=0.6$