Question 1025954
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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