Q.3.36 - A First Course in Probability

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 $C$?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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,

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

$=\frac{70}{140}$

$=\frac{1}{2}$

Step 3: Final answer

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