Question 1107254
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In both cases, you are choosing 2 out of the 18 people in the group, so the denominator of the probability fraction is "18 choose 2":
{{{C(18,2) = (18*17)/(2*1) = 153}}}<br>
a) If both are men, then you are choosing 2 of the 10 men and 0 of the 8 women.  The numerator of the probability fraction is
{{{C(10,2)*C(8,0) = 45*1 = 45}}}
The probability that both are men is 45/153 = 9/17.<br>
b) "at least one is a woman" is the opposite (complement) of "both are men".  So the probability  that at least one is a woman is 1 - 9/17 = 8/17.