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triplec · Jun 26, 2012, 07:52 AM

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

ebaines · Jun 26, 2012, 09:25 AM

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?

triplec · Jun 26, 2012, 12:43 PM

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?

yes