in the 107th congress the senate consisted of 13 women and 87 men if a lobbyist for the tobacco industry randomly selects three different senators what is the probability that they are all women and can you show your work please

We won't do your homework for you, but will give you a hint to get you started. Suppose the question was a little different - to find the probability that if a lobbyist randomly selects 2 people that they are both men. This is equal to the probability that the first pick is a man times the probability that the second pick is a man. For the first pick there are 87 men out of 100 possible choices, so the probability of picking a man is 87/100. Once you have picked one man, that leaves 86 out of the remaining 99 who are men, so the probability that the second pick is a man is 86/99. Hence the probability that both picks are men is (87/100) x (86/99).

Do you see how that works, and can you apply this technique to your problem?

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Originally Posted by ebaines

We won't do your homework for you, but will give you a hint to get you started. Suppose the question was a little different - to find the probability that if a lobbyist randomly selects 2 people that they are both men. This is equal to the the probability that the first pick is a man times the probability that the second pick is a man. For the first pick there are 87 men out of 100 possible choices, so the probability of picking a man is 87/100. Once you have picked one man, that leaves 86 out of the remaining 99 who are men, so the probability that the second pick is a man is 86/99. Hence the probability that both picks are men is (87/100) x (86/99).

Do you see how that works, and can you apply this technique to your problem?

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yes