7. There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains :
(i) at least one girl
(ii) one boy and one girl
(iii) only boys
Sol. Let three boys be denoted as B1, B2, B3 and two girls be denoted as G1, G2. A committee of two can be formed in the following ways
∴ S = { B1 B2, B1 B3, B1 G1, B1 G2, B2 B3, B2 G1, B2 G2, B3 G1, B3 G2, G1 G2 }
∴ n (S) = 10
(i) Let A be event that committee contains atleast one girl
A = { B1 G1, B1 G2, B2 G1, B2 G2, B3 G1, B3 G2, G1 G2 }
n (A) = 7
P (A) = n (A)/n (S)
∴ P (A) = 7/10
(ii) Let B be the event that committee contains one boy and one girl
B = { B1 G1, B1 G2, B2 G1, B2 G2, B3 G1, B3 G2 }
n (B) = 6
P (B) = n (B)/n (S)
∴ P (B) = 6/10
∴ P (B) = 3/5
(iii)Let C be the event that committee contain only boys
C = { B1 B2, B1 B3, B2 B3 }
n (C) = 3
P (C) = n (C)/n (S)
∴ P (C) = 3/10
