SOLUTION: PLEASE HELP!! I REALLY NEED HELP! A jury pool consists of 30 people, 16 men and 14 women. Compute the probability that a randomly selected jury of 12 people is all male. (Give y

Question 1048812: PLEASE HELP!! I REALLY NEED HELP!
A jury pool consists of 30 people, 16 men and 14 women. Compute the probability that a randomly selected jury of 12 people is all male. (Give your answer as a fraction.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
number of ways you can get 12 men out of 16 men is c(16,12) = 1820.

number of ways you can get 14 jurors out of 30 people is c(30,12) = 145422675.

the probability that the jury will consist of all men is 1820 / 86493225 = 2.104211052 * 10^-5 which is equal to .00002104211052.

look at it another way.

the probability that you can draw 1 man out of 30 jurors when 16 of them are men would be 16/30.

the probability that you will draw 12 men in a row would then be:

16/30 * 15/29 * 14/28 * 13/27 * 12/26 * 11/25 * 10/24 * 9/23 * 8/22 * 7/21 * 6/20 * 5/19

that's equal to .00002104211052

same answer either way, so the solution looks good.

the calculator might show the answer as 2.104211052 * 10^(-5).

that's the same as 2.104211052 / 100,000 which is equal to .00002104211052.

the probability of any occurrence is the number of ways it can occur divided by the total number of ways all possible combinations can occur.

that would be the number of possible ways 12 men can occur divided by the number of ways 12 jurors can occur whether or not they are men or women.

c(16,12) is the number of ways you can get 12 men out of 16 possible men.

c(30,12) is the number of ways you can get 12 jurors out of 30 possible juror whether or not they are men or women.

the combination formula is c(n,x) = n! / (x! * (n-x)!)

when you have 16 possible men and need to select 12 out of them, the formula becomes c(16,12) which is equal to 16! / (12! * 4!) which is equal to 1820

when you have 30 possible jurors and need to select 12 out of them, the formula becomes c(30,12) = 30! / (18! * 12!) which is equal to 86493225.

1820 / 86493225= 2.104211052 * 10^(-5) which is equal to .00002104211052.

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