A youth group has 7 boys

Question

and 5 girls. Experiment is select 5 people at random from the group. Let X be the number
of boys in the selected 5 people.
(a) Find the probability of exactly 1 boy, i.e., P([X = 1]).
(b) Find the probability of exactly 2 boy, i.e., P([X = 2]).
(c) Find the probability of at least one boy, i.e., P([X ≥ 1]).
(d) Find the expected value
 X
and the standard deviation
 X

Answer 1

prob(exactly one boy)
= C(7,1)xC(5,4)/C(12,5)
= 7(5)/792
= 35/792

prob(exactly 2 boys)
= C(7,2)xC(5,3)/792
= 21(10)/792
= 35/132

at least one boy
= 1 - prob(all girls)
= 1 - 1/792
=791/792