SOLUTION: Two people are selected from a group of eight women and ten men. Find the probability that a) Both are men. b) At least one is a woman.

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Question 1107254: Two people are selected from a group of eight women and ten men. Find the probability that
a) Both are men.
b) At least one is a woman.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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%2818%2C2%29+=+%2818%2A17%29%2F%282%2A1%29+=+153

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%2810%2C2%29%2AC%288%2C0%29+=+45%2A1+=+45
The probability that both are men is 45/153 = 9/17.

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.