Given a population of 18 men and 7 women, which of the two following scenarios is more likely?
What will be an ideal response?
A: A team of six people is assembled, of which three are men.
B: A team of ten people is assembled, of which five are men.
p(X=x) = (r choose x) (N-r choose n-x) / (N choose n)
A: p(X=3) = (18 choose 3) (25-18 choose 6-3) / (25 choose 6) = 816 * 35 / 177100 = .161
B: p(X=5) = (18 choose 5) (25-18 choose 10-5) / (25 choose 10) = 8568 * 21 / 3268760
= .055
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