Suppose that 7 female and 7 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 14 finalists, what is the probability of selecting
(A) 3 females and 2 males?
(B) 4 females and 1 male?
(C) 5 females?
(D) At least 4 females?
(A) The probability of selecting 3 females and 2 males is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
(B) The probability of selecting 4 females and 1 male is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
(C) The probability of selecting 5 females is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
(D) The probability of selecting at least 4 females is approximately
(Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：We are given that there are 7 female and 7 male applicants who have been successfully screened for 5 positions. We are asked to find the probability of selecting a certain number of females and males for these positions.

Step 2 ：We can solve this problem using the combination formula, which is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 3 ：For each part of the question, we need to calculate the number of ways to choose a certain number of females and males, and then divide by the total number of ways to choose 5 applicants from 14.

Step 4 ：For 3 females and 2 males, we need to calculate \(C(7, 3) * C(7, 2)\).

Step 5 ：For 4 females and 1 male, we need to calculate \(C(7, 4) * C(7, 1)\).

Step 6 ：For 5 females, we need to calculate \(C(7, 5)\).

Step 7 ：For at least 4 females, we need to calculate the sum of the probabilities for 4 and 5 females, which is \(C(7, 4) * C(7, 1) + C(7, 5)\).

Step 8 ：The total number of ways to choose 5 applicants from 14 is \(C(14, 5)\).

Step 9 ：After calculating these probabilities, we find that the probability of selecting 3 females and 2 males is approximately \(0.367\), the probability of selecting 4 females and 1 male is approximately \(0.122\), the probability of selecting 5 females is approximately \(0.010\), and the probability of selecting at least 4 females is approximately \(0.133\).

Step 10 ：Final Answer: (A) The probability of selecting 3 females and 2 males is approximately \(\boxed{0.367}\). (B) The probability of selecting 4 females and 1 male is approximately \(\boxed{0.122}\). (C) The probability of selecting 5 females is approximately \(\boxed{0.010}\). (D) The probability of selecting at least 4 females is approximately \(\boxed{0.133}\).