SOLUTION: In a large crowd, there are three times as many men as women. Three people are choosen at random. Assuming that there are so many people that choosing three has a negligible effect

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Question 1156252: In a large crowd, there are three times as many men as women. Three people are choosen at random. Assuming that there are so many people that choosing three has a negligible effect on the proportion of men to women, find the probability that they are
a. all men b.2woman and 1man.
Assist in explaining this "Assuming that there are so many people that choosing three has a negligible effect on the proportion of men to women", please.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
all men=(1/8), or 1/2 ^3
2 women and 1 man. Three ways to happen, each with probability of 1/8 and probability is 3/8
If the population is large enough, choosing a man will not make a difference on the second choice, where there is one less man. The population can be considered so large that removing 1 does not change the distribution significantly.
Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.

(1)  Since there are three times as many man as women, 

         - the probability that the randomly chosen person is a man is  ,  and

         - the probability that the randomly chosen person is a woman is  .



     THEREFORE, the probability that three randomly selected persons all are the men is  P =  =  = 0.421875.



(2)  the probability that three randomly selected persons are (2 women and 1 men) is  P =  =  = 0.14.

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The calculated numbers in the post by @Boreal are incorrect, so IGNORE it, for your safety.

He misread the problem.

He is so hurry that has no time to read the problem properly.



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