Question

If $P\left(A\right)=0.60,P(A\cup B)=0.85andP(A\cap B)=0.05,findP\left(B\right)$

Short answer

The probability is$0.30$

Step-by-step solution

Step 1. Given Information  

The given data is$P\left(A\right)=0.60,P(A\cup B)=0.85andP(A\cap B)=0.05$

Step 2. Calculation

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

$$\begin{gathered} P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B) \\ 0.85=0.60+P\left(B\right)-0.05 \\ 0.85-0.55=P\left(B\right) \\ P\left(B\right)=0.30 \end{gathered}$$