There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains at least one girl.

There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains:

a. at least one girl.
b. one boy and one girl.
c. only boys. 



Solution:
Since a committee of two is be formed from three boys and two girls,



Sample Space = { B1B2, B1B3, B1G1, B1G2, B2B3, B2G1, B2G2, B3G1, B3G2, G1G2}

a. Let A = Event of forming a committee which contains atleast one girl

A = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, G1G2}

n(A) = 7

P(A)
=
n(A)
=
7
n(S)
10


b. Let B = Event that the committee contains one boy and one girl.
B = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, }

n(B) = 6


P(B)
=
n(B)
=
6
=
3
n(S)
10
5


c. Let C = Event that the committee contains only boys.

C = { B1B2, B1B3, B2B3}

n(C) = 3


P(C)
=
n(C)
=
3
=
3
n(S)
10
10