SSC BOARD PAPERS IMPORTANT TOPICS COVERED FOR BOARD EXAM 2024

### 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