SOLUTION: A company intends to form its CSR committee with 4 members, from a pool of 14 managers (5 women and 9 men). A) What is the probability that all members of the CSR committee would

Question 1025954: A company intends to form its CSR committee with 4 members, from a pool of 14 managers (5 women and 9 men).
A) What is the probability that all members of the CSR committee would be female managers?
B) What is the probability that all members of the CSR committee would be male managers?
C) What is the probability of having at least 3 female managers in the CSR committee?
D) How many male managers should be removed from the pool so that board of directors can be 90% confident of having at least half of the CSR commitee represented by female managers?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the formulas will be:

formula 1.
p(exactly 4 women) = 5c4 / 14c4 = .004995...
formula 2.
p(exactly 4 men) = 9c4 / 14c4 = .125874...

formula 3.
p(exactly 3 women) = (5c3 * 9c1) / 14c4 = .089910...

formula 4.
p(at least 3 women) = p(exactly 3 women) + p(exactly 4 women) = formula 3 plus formula 1 = .089910... + .004995... = .094905...

this can be seen in the worksheet by adding up the cells F8 and F9.
F8 is column F row 8.
F9 is column F row 9.

in order for the probability to be equal to or greater than 90% that there will be at least 2 women on the team, then the number of men has to be reduced to 3.

this means that 6 of the men must be removed from the pool.

when there are only 3 men in the pool, then the probability that the team will consist of all men becomes equal to 0 because the team requires 4 members and there are only 3 men available.

the following worksheet summarizes the calculations.

the worked up probabilities are in the worksheet.

p(0 women) means p(4 men)
p(1 woman) means p(1 woman and 3 men).
p(2 women) means p(2 women and 2 men).
p(3 women) means p(3 women and 1 man).
p(4 women) means p(4 women and 0 men).

column F contains the results for 5 women and 9 men, shown as 5w9m.

the other columns follow the same convention.

5w8m means 5 women and 8 men, etc.

here's the worksheet.

$$$

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