From a group of 2 boy and 3 girls, two children are selected at random. Describe the events. A = both selected children are girls. B= the selected group consists of one boy and one girl. C= at least one boy is selected. Which pairs (s) of events is (are) mutually exclusive?

Explanation

Let us name the boys as `B_(1) and B_(2)`, and the girls as `G_(1), G_(2) and G_(3)`.
Then
`S = {B_(1)B_(2), B_(1)G_(1), B_(1)G_(2), B_(1)G_(3), B_(2)G_(1), B_(2)G_(2), B_(2)G_(3), G_(1)G_(2), G_(1)G_(3), G_(2)G_(3)}`
We have
(i) `A = {G_(1)G_(2), G_(1)G_(3), G_(2)G_(3)}`
(ii) `B = {B_(1)G_(1), B_(1)G_(2), B_(1)G_(3), B_(2)G_(1), B_(2)G_(2), B_(2)G_(3)}`
(iii) `C = {B_(1)G_(1), B_(1)G_(2), B_(1)G_(3), B_(2)G_(1), B_(2)G_(2), B_(2)G_(3), B_(1)B_(2)}`
Clearly, `A nn B = phi and A nn C = phi`.
Hence, (A, B) and (A, C) are mutually exclusive events.