SOLUTION: A room contains five men and four women. Two people are selected at random with no replacements between selections. 1. Find the probability that the first person selected is a man

Question 291857: A room contains five men and four women. Two people are selected at random with no replacements between selections.
1. Find the probability that the first person selected is a man and the second is a woman.
2. Find the probability that all the people selected are men.
3. Find the probability that the second person selected is a woman, given that the first to be selected was a woman.
4. Find the probability that one man and one woman are selected.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A room contains five men and four women. Two people are selected at random with no replacements between selections.
1. Find the probability that the first person selected is a man and the second is a woman.
Ans: (5/9)(4/8) = 20/72 = 5/18
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2. Find the probability that all the people selected are men.
Ans: 5C2/9C2 = 10/36 = 5/18
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3. Find the probability that the second person selected is a woman, given that the first to be selected was a woman.
Ans: P(w|w) = P(2 women)/P(women) = [4C2/9C2]/[4/9] = (6/36)/(4/9) = 3/8
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4. Find the probability that one man and one woman are selected.
P(1m and 1 w) = 1-[P(2men)+P(2women)] = 1-[(5/18)+(1/6)] = 10/18 = 5/9
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Cheers,
Stan H.
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