Probability of a woman employee resigning from store C

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

In this problem, we are given the gender ratios and number of employees in three stores, and asked to calculate the probability that a resigning woman employee is from store C.

Let's begin by calculating the total number of women employees across all three stores:

Total number of women employees = (5050/100) + (7560/100) + (100*70/100) = 25 + 45 + 70 = 140

We know that a woman employee has resigned. The probability of this happening can be calculated using Bayes' theorem, which states that the probability of an event A given event B is equal to the probability of both events occurring divided by the probability of event B occurring:

P(C | W) = P(W | C) * P(C) / P(W)

where P(C | W) is the probability of the woman employee working in store C given that she has resigned, P(W | C) is the probability of a woman employee resigning from store C, P(C) is the probability of an employee working in store C, and P(W) is the probability of a woman employee resigning.

We know that the probability of an employee working in store C is 100/225, since there are a total of 225 employees across all three stores, and 100 of them work in store C. We also know that the probability of a woman employee resigning is equal to the total number of women employees divided by the total number of employees across all three stores, which is 140/225.