Favorableoutcome=(1girl,1girl);(1boy,1girl);(1girl,1boy)=3
total outcome=5
p(atleast 1 girl)= favorable outcome÷total outcome
= 3/5

Problem Statement:
From a group of 3 girls and 2 boys, two children are selected at random. Find the probability such that at least one girl is selected.

Solution:

To find the probability of selecting at least one girl, we need to consider two scenarios:

1. Selecting one girl and one boy.
2. Selecting two girls.

Step 1: Calculate the total number of possible outcomes.

The total number of ways to select 2 children from a group of 5 is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)

In this case, n = 5 (total number of children) and r = 2 (number of children to be selected).

C(5, 2) = 5! / (2!(5-2)!) = (5 * 4 * 3 * 2!) / (2! * 3 * 2!) = 10

Therefore, there are 10 possible outcomes when selecting 2 children from the group.

Step 2: Calculate the number of favorable outcomes.

Scenario 1: Selecting one girl and one boy.
There are 3 girls and 2 boys in the group. We can select 1 girl and 1 boy in the following ways:

- Girl, Boy: G1, B1
- Girl, Boy: G1, B2
- Girl, Boy: G2, B1
- Girl, Boy: G2, B2
- Girl, Boy: G3, B1
- Girl, Boy: G3, B2

Therefore, there are 6 favorable outcomes in this scenario.

Scenario 2: Selecting two girls.
There are 3 girls in the group. We can select 2 girls in the following ways:

- Girl, Girl: G1, G2
- Girl, Girl: G1, G3
- Girl, Girl: G2, G3

Therefore, there are 3 favorable outcomes in this scenario.

Step 3: Calculate the probability.

The probability is given by the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the number of favorable outcomes is 6 + 3 = 9, and the total number of possible outcomes is 10.

Probability = 9 / 10 = 0.9

Therefore, the probability of selecting at least one girl is 0.9 or 90%.