Probability Question Needed to be Answered

[jensen02431]

A youth group has eight boys and six girls. If a state of four officers is selected, find the probability that...

a.) Three are girls?

b.) Two are girls?

c.) At most 2 are girls?

[curquht]

A youth group has eight boys and six girls. If a state of four officers is selected, find the probability that...

a.) Three are girls?

b.) Two are girls?

c.) At most 2 are girls?

P(x=3) = (8 choose 1)x(6 choose 3)/(14 choose 4)

Because there are 8 boys to choose from and only 1 will get chosen, 6 girls to choose from and 3 get chosen, over the total number of people from which 4 people can be chosen.

p(x=2) = (8 choose 2)x(6 choose 2)/(14 choose 4)
similar to reason given above

p(x<=2) = p(x=0) + p(x=1) + p(x=2)
= (8 choose 4)x(6 choose 0)/(14 choose 4) + (8 choose 3)x(6 choose 1)/(14 choose 4) + (8 choose 2)x(6 choose 2)/(14 choose 4)