SOLUTION: Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 20 men and 5 women. (Enter your pr

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Question 1148101: Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 20 men and 5 women. (Enter your probabilities as fractions.)
(a) Find the probability that both appointees are men.
(b) Find the probability that one man and one woman are appointed.
(c) Find the probability that at least one woman is appointed.
Answer by greenestamps(13200) About Me  (Show Source):
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(a) both men....

P(1st is a man) = 20/25
P(2nd is a man) = 19/24
P(both are men) = (20/25)*(19/24); simplify as required

OR...

%28C%2820%2C2%29%2AC%285%2C0%29%29%2F%2825C2%29 [choose 2 of the 20 men and 0 of the 5 women]

(b) one man and one woman....

P(man first and woman second) = (20/25)*(5/24)
P(woman first and man second) = (5/25)*(20/24)
P(one man and one woman) = (20/25)*(5/24) + (5/25)*(20/24); simplify as required

OR...

%28C%2820%2C1%29%2AC%285%2C1%29%29%2F%2825C2%29 [choose 1 of the 20 men and 1 of the 5 women]

(c) at least one woman...

P(at least one woman) = 1 - P(both men)

P(both men) was calculated in part (a)