Chapter 13.3, Problem 46AYU

In Problems 45-48, find the probability of the indicated event if $P\left(A\right)=0.25$ and

$P\left(B\right)=0.45$

$P\left(A\cap B\right)ifP\left(A\cup B\right)=0.6$

To determine

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

Answer to Problem 46AYU

Solution:

$0.10$

Explanation of Solution

Given:

$P\left(A\right)=0.25, P\left(B\right)=0.45, P\left(A\cup B\right)=0.6$

Formula used:

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

Calculation:

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

$0.6=0.25+0.45-P\left(A\cap B\right)$

$P\left(A\cap B\right)=.25+.45-0.6$

$P\left(A\cap B\right)=.10$