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




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


