Question

A lawsuit has been brought by female managers of the company. Recently the company decided to promote three of the eight mid-level managers to top vice president positions. Of the mid-level managers, five for woma. Of the mid-level managers, five where woman and three were men, get all of the positions went to the men were woman and three were men, get all of the positions went to the men, . The lawyer for the woman believes that they have the case if the probability of only men getting these emotions by chance alone is less than 5%. Do the female employees have a case? Just the fire answer. The lawyer for the woman believes that they have the case if the probability of only men getting these through promotions by the chance alone is less than 5%. Do the female employees have a case? Justify your answer

Answer 1

Answer on question #55304 – Math – Statistics and Probability

Question

A lawsuit has been brought by female managers of a company. Recently the company decided to promote three of eight mid-level managers to top vice-president positions. Of the eight mid-level managers, five were women and three were men, yet all of the promotions went to the men. The lawyer for the women believes that they have a case if the probability of only men getting these three promotions by chance alone is less than 5%. Do the female employees have a case?

Solution

From the question we know that the probability of getting the promotion for every employee is the same. Thus, the probability of a man getting the first promotion is $\frac{3}{8}$, because we have 3 desired variants of 8 possible ones. Then the probability of a second man getting a promotion will be $\frac{2}{7}$, as the number of all possible variants will now be less – one man is gone from the pool (so we will have one variant less in both desired and possible pools). Finally, the probability of a third man getting a promotion is now $\frac{1}{6}$ (exactly as before – minus one variant from both desired and possible pools). To get the total chance, we must now multiply all the probabilities, and we will get

$$P_f = \frac{3}{8} \cdot \frac{2}{7} \cdot \frac{1}{6} = \frac{6}{336} = \frac{1}{56} \approx 1.8\% < 5\%$$

Answer: chance is less than five percent, so female employees have a case.

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