Chapter 13.3, Problem 50AYU

To determine

To find: The probability of $P\left(A\right)$.

Answer to Problem 50AYU

Solution:

$P\left(A\right)=0.5$

Explanation of Solution

Given:

$P\left(B\right)=0.30, P\left(A\cup B\right)=0.65 \text{and} P\left(A\cap B\right)=0.15$

Formula used:

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

Calculation:

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

$0.65=P\left(A\right)+0.3-0.15$

$P\left(A\right)=0.5$