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14. A jury pool consists of 27 people, 15 men and 12 women. Compute the probability that a randomly selected jury of 12 people is all male.

14. A jury pool consists of 27 people, 15 men and 12 women. Compute the probability-example-1
User DaoWen
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1 Answer

7 votes

Given:

Total number of people (n)=27

men =15

women=12


^{}Totalnumberofwaystoselect12peoplefrom24=^(27)C_(12)
=(27!)/(12!(15!))
=(27*26*25*24*23*22*21*20*19*18*17*16*15!)/(12*11*10*9*8*7*6*5*4*3*2*1*15!)
=3*13*23*3*20*19*17
=17383860
NO\text{ of ways to select 12 male=}^(15)x_(12)
=(15!)/(12!(3!))
=(15*14*13*12!)/(12!3!)
=5*7*13
=455

Probability of selecting the 12 males is P(A)


P(A)=(455)/(17383860)
P(A)=(7)/(267444)

User Oerkelens
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