Question

Stores $A,B$, and $C$have $50,75$, and $100$employees, respectively, and $50,60$, and $70$percent of them respectively are women. Resignations are equally likely among all employees, regardless of sex. One woman employee resigns. What is the probability that she works in store $C$?

Short answer

The probability that she works in store$C$is$\frac{1}{2}$.

Step-by-step solution

Given information

Stores $A,B$, and $C$have $50,75$, and $100$employees, respectively, and $50,60$, and $70$ percent of them respectively are women.

Solution

The table of the employee's work in the store is given below,

Number of employees	Women
$A:50$	$0.5$
$B:75$	$0.6$
$C:100$	$0.7$

Then the probability will be,

$P(C\mid \text{Women})=\frac{0.7\times 100}{0.5\times 50+0.6\times 75+0.7\times 100}$

$=\frac{70}{140}$

$=\frac{1}{2}$

Final answer

The probability that she works in store $C$ is $\frac{1}{2}$.