Question

For two events A and B, suppose $P\left(A\right)=.7$,$P\left(B\right)=.5$,$P(A\cap B)=0.4$Find$P(A\cup B)$.

Short answer

The value of $P(A\cup B)$is 0.8.

Step-by-step solution

Important formula

The require formula for union is $\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cup }\mathit{B}\mathbf{)}\mathbf{=}\mathit{P}\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{+}\mathit{P}\mathbf{\left(}\mathit{B}\mathbf{\right)}\mathbf{-}\mathit{P}\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{B}\mathbf{)}$.

Finding P(A∪B) 

Here, $P\left(A\right)=.7$, $P\left(B\right)=.5$, $P\left(A\cap B\right)=.4$.

Therefore,

$$\begin{gathered} P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ =0.7+0.5-0.4 \\ =0.8 \end{gathered}$$

Thus required probability is $P\left(A\cup B\right)=0.8$.