Question

Store A, B and C have 50, 75 and 100 employees, and respectively,50,60,70 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?

Answer 1

To find the probability that the woman who resigned works in store C, we can use Bayes' theorem. Using the given information, we calculate the individual probabilities and substitute them into the formula to find the final probability. The probability that the woman who resigned works in store C is approximately 0.6604.

Step-by-step explanation:

To find the probability that the woman who resigned works in store C, we need to use Bayes' theorem. Let's define the events:

A: The woman who resigned works in store C

B: The woman who resigned is a woman

We are given the following information:

P(A|B) = 0.70 (probability that the woman who resigned works in store C given she is a woman)

P(A') = 0.30 (probability that the woman who resigned does not work in store C)

P(B|A') = 0.60 (probability that the woman who resigned is a woman given she does not work in store C)

To find P(A|B), we will use Bayes' theorem: P(A|B) = (P(B|A) * P(A)) / P(B)

P(B) can be calculated as:

P(B) = P(A|B) * P(B) + P(A'|B) * P(B)

P(B) = (0.70 * 0.50) + (0.60 * 0.30) = 0.35 + 0.18 = 0.53

Finally, substituting the values in Bayes' theorem:

P(A|B) = (0.70 * 0.50) / 0.53 = 0.35 / 0.53 = 0.6604 (rounded to four decimal places)

Therefore, the probability that the woman who resigned works in store C is approximately 0.6604.