There are three boys and three girls. An environment committee of two is to be formed. Write the sample space S, the number of sample points n(S). Also find P(A) where A is the event that the committee should contain atleast one girl.

Solution:

There are 3 boys and 3 girls from which a environment committee of two is to be formed.

B1, B2, B3, G1, G2, G3 are given

∴ Sample space = {B1B2, B1B3, B1G1, B1G2, B1G3, B2B3, B2G1, B2G2, B2G3, B3G1, B3G2, B3G3, G1G2, G1G3, G2G3}

∴ n(S) = 15

Now, A = Event of forming a committee contains atleast one  girl.

∴ A = { B1G1, B1G2, B1G3, B2G1, B2G2, B2G3, B3G1, B3G2, B3G3, G1G2, G1G3, G2G3}

∴ n(A) = 12

∴ P(A) = n(A)/n(S)

∴ P(A) = 12/15

∴ P(A) = 4/5