SOLUTION: A jury pool consists of 34 people, 17 men and 17 women. Compute the probability that a randomly selected jury of 12 people is all male. PLEASE EXPLAIN the steps!! I'm so c

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Question 1200365: A jury pool consists of 34 people, 17 men and 17 women. Compute the probability that a randomly selected jury of 12 people is all male.


PLEASE EXPLAIN the steps!! I'm so clueless on this question.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: Approximately 0.00001128468024
Round however you need to, or however your teacher instructs.


Explanation:

You'll need a calculator that has the nCr combination function on it.

Here is a free online alternative
https://www.omnicalculator.com/statistics/combination
Ignore the "combinations with repetitions" portion. For this problem, repetitions aren't allowed.

Using a calculator like that will show...
  • 17C12 = 6,188 different ways to get a jury of all men
  • 34C12 = 548,354,040 different ways to get a jury (men and/or women)
Divide the two results:
6188/548354040 = 0.00001128468024

Extra info:
The nCr combination formula is
nCr = (n!)/(r!(n-r)!)
The exclamation marks indicate factorial.

Example calculation:
n C r = (n!)/(r!(n-r)!)
17 C 12 = (17!)/(12!*(17-12)!)
17 C 12 = (17!)/(12!*5!)
17 C 12 = (17*16*15*14*13*12!)/(12!*5!)
17 C 12 = (17*16*15*14*13)/(5!)
17 C 12 = (17*16*15*14*13)/(5*4*3*2*1)
17 C 12 = (742560)/(120)
17 C 12 = 6188

Answer by ikleyn(52866) About Me  (Show Source):
You can put this solution on YOUR website!
.
A jury pool consists of 34 people, 17 men and 17 women.
Compute the probability that a randomly selected jury of 12 people is all male.
~~~~~~~~~~~~~~~~~~~~~~~~ 

It can be solved in different way, too.


The probability that 1-st selected member is a man is  17%2F34.

The probability that 2-nd selected member is a man given that 1-st is a man is  16%2F33.

The probability that 3-rd selected member is a man given that 1-st and 2-nd are men is  15%2F32.

 . . . and so on and so on . . . 


Then the final probability is the product of these 12 factors

    P =  = 1.12847E-05.

Simple ?

You may know nothing and apply only your common sense.


        (Or  DEVELOP  your common sense).