Question

Personnel selection. Suppose that 7 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 12 âfinalists, what is the probability of selecting â

(A) 3 females and 2â males? â
(B) 4 females and 1â male? â
(C) 5â females?
â(D) At least 4â females?

Answer 1

The question involves calculating the probabilities of different combinations of females and males being selected for positions using the hypergeometric distribution, a concept in mathematics related to probability without replacement from two distinct groups.

Step-by-step explanation:

The question is related to the concept of probability in mathematics, specifically the use of the hypergeometric distribution, which is appropriate when sampling without replacement from a finite population divided into two groups. To calculate the probability of various combinations of female and male applicants selected for the positions, we need to use the hypergeometric probability formula:

1. For part (A), calculating the probability of selecting 3 females and 2 males:
2. For part (B), calculating the probability of selecting 4 females and 1 male:
3. For part (C), calculating the probability of selecting 5 females:
4. For part (D), calculating the probability of selecting at least 4 females (which includes scenarios of selecting 4 or 5 females):

These calculations involve combinations (denoted as C(n, k)) and the formula for hypergeometric probability, which is:

Hypergeometric Probability = [C(group1 size, group1 subset size) * C(group2 size, group2 subset size)] / C(total population size, total subset size)