Question

If$P\left(B\right)=0.30,P(A\cup B)=0.65andP(A\cap B)=0.15,findP\left(A\right)$

Short answer

The probability is$0.50$

Step-by-step solution

Step 1. Given Information  

The given data is$P\left(B\right)=0.30,P(A\cup B)=0.65andP(A\cap B)=0.15$

Step 2. Calculation

Substitute the values in the formula to find the required value,

$$\begin{gathered} P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B) \\ 0.65=P\left(A\right)+0.30-0.15 \\ P\left(A\right)=0.65+0.15-0.30 \\ P\left(A\right)=0.50 \end{gathered}$$