SOLUTION: A jury consists of five men and seven women. Four are selected at random for an interview. a) Find the probability that all four selected people are men. b) Find the probability

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Question 1175829: A jury consists of five men and seven women. Four are selected at random for an interview.
a) Find the probability that all four selected people are men.
b) Find the probability that two men and two women are selected.
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
 Jury-12 People: 5M and 7W
Select 4(at random)  12C4 = 495,  all possible ways this can be done.

P(all men) = (5C4)(7C0)/(12C4) = 5/495

P(2 M & 2 W) = (5C2)(7C2)/(12C4) = 10*21/495

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The total number of ways of choosing 4 of the 12 people is

C%2812%2C4%29+=+495

The number of ways of choosing 4 of the 5 men and 0 of the 7 women is

%28C%285%2C4%29%2AC%287%2C0%29%29+=+5%2A1+=+5

So the probability of choosing 4 men is 5/495.

The number of ways of choosing 2 of the 4 men and 2 of the 4 women is

%28C%285%2C2%29%2AC%287%2C2%29%29+=+10%2A21+=+210.

So the probability of choosing 2 men and 2 women is 210/495.

Simplify the two answers if needed.

When you are first learning to solve problems like this, you can get further practice and also get confirmation that your calculations are correct by finding the probabilities of all other combinations of men and women and verifying that the sum of all the probabilities is 1.

3 men and 1 woman: C%285%2C3%29%2AC%287%2C1%29+=+10%2A7+=+70; probability 70/495

1 man and 3 women: C%285%2C1%29%2AC%287%2C3%29+=+5%2A35+=+175; probability 175/495

0 men and 4 women: C%285%2C0%29%2AC%287%2C4%29+=+1%2A35+=+35; probability 35/495

Sum of all the probabilities: (5+70+210+175+35)/495 = 495/495 = 1