Q) From a group of 3 boys and 2 girls we select two children. What is the set representing the event:
i. one girl is selected
ii. at least one girl is selected

Ans: 

Let’s first find out all possible sets of selecting two children:
Let 3 boys are B₁, B₂, B₃ and 2 girls are G₁, G₂, then the all possible outcomes sets are:

{B₁ G₁, B₁ G₂, B₂ G₁, B₂ G₂, B₃ G₁, B₃ G₂, B₁ B₂, B₁ B₃, B₂ B₃, G₁ G₂}

i. One girl is selected:
Next, let’s take out all the outcomes which have only 1 girl in it.

The favourable events for selecting one girl are:

{B₁ G₁, B₁ G₂, B₂ G₁, B₂ G₂, B₃ G₁, B₃ G₂}

ii. At least one girl is selected:
Next, let’s take out all the outcomes which have at least 1 girl in it.

It means, we need to consider all the outcomes with 1 girl + all the outcomes with 2 girls

Hence, the favourable events for selecting at least one girl are:

{B₁ G₁, B₁ G₂, B₂ G₁, B₂ G₂, B₃ G₁, B₃ G_2, G₁ G_2,}