SOLUTION: Personnel selection. Suppose that 8 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the ​finalists, wh

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Question 1197702: Personnel selection. Suppose that 8 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the ​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?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Overall, 5 of the 14 applicants are to be chosen. The number of ways of doing that is "14 choose 5":

C%2814%2C5%29=%2814%2A13%2A12%2A11%2A10%29%2F%285%2A4%2A3%2A2%2A1%29=2002

The probability of a particular outcome is the number of ways of getting that outcome, divided by that total number of possible outcomes.

The numbers of ways of getting particular outcomes all involve similar straightforward calculations.

(1) To get 0 females and 5 males, you need to choose 0 of the 8 females (8 choose 0) AND 5 of the 6 males (6 choose 5).
The number of ways of getting 0 females and 5 males is C%288%2C0%29%2AC%286%2C5%29+=+%281%29%286%29+=+6
P(0 females) = 6/2002 (simplify if necessary)

(2) To get 1 female and 4 males, you need to choose 1 of the 8 females (8 choose 1) AND 4 of the 6 males (6 choose 4).
The number of ways of getting 1 female and 4 males is C%288%2C1%29%2AC%286%2C4%29+=+%288%29%2815%29+=+120
P(0 females) = 120/2002 (simplify if necessary)

Calculate the probabilities for the other outcomes in the same manner, then answer the questions.

Note that you can get good practice in making this kind of calculations by finding the probabilities of all the possible outcomes and verifying that the sum of those probabilities is 1.

Further note that, if you do in fact calculate the probabilities for all the possible outcomes, it will be easier to verify that the sum is 1 if you do NOT simplify each of the probabilities; leave them all with denominator 2002 and verify that the sum of the numerators is 2002.