from a group of ten boys and twelve...

Problema Solution

from a group of ten boys and twelve girls, a committee of four students is chosen at random. What is the probability that:

a. all four members of the committee will be girls?

b. all four member of the committee will be boys?

c. there will be a least one girl on the committee?

P(all are girls) = C(12, 4)/C(22, 4)

C(12, 4) = 12!/(4!(12 - 4)!) = 9*10*11*12/4! = 495

C(22, 4) = 22!/(4!(22 - 4)!) = 19*20*21*22/4! = 7315

P(all are girls) = 495/7315

P(all are girls) = 0.06767

P(all are boys) = C(10, 4)/C(22, 4)

C(10, 4) = 10!/4!(10 - 4)!)

C(10, 4) = 7*8*9*10/4!

C(10, 4) = 210

P(all are boys) = 210/7315

P(all are boys) = 0.02871

P(there is at leas 1 girl) = 1 - P(there are no girls) = 1 - P(all are boys)

P(there is at leas 1 girl) = 1 - 0.02871

P(there is at leas 1 girl) = = 0.97129

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