Introduction:
In this problem, we are given a group of two boys and three girls, and we need to find the probability of selecting at least one boy when two children are chosen randomly from the group.

Step 1: Determining the sample space:
The sample space is the set of all possible outcomes when two children are chosen randomly from the group. Since we are selecting two children, the sample space will consist of all possible combinations of two children from the group.

Step 2: Finding the favorable outcomes:
To find the favorable outcomes, we need to determine the combinations that result in at least one boy being selected. There are three scenarios in which we can have at least one boy:
1. Selecting one boy and one girl
2. Selecting two boys
3. Selecting two girls (not favorable)

Step 3: Calculating the probability:
The probability can be calculated using the formula:
Probability = Number of favorable outcomes / Total number of outcomes

Step 4: Calculating the number of favorable outcomes:
1. Selecting one boy and one girl:
We have two boys and three girls in the group. For this scenario, we can choose one boy in 2 ways and one girl in 3 ways. Therefore, the number of favorable outcomes is 2 * 3 = 6.

2. Selecting two boys:
We have two boys in the group. For this scenario, we can choose two boys in 2 ways. Therefore, the number of favorable outcomes is 2.

Step 5: Calculating the total number of outcomes:
The total number of outcomes can be calculated using the combination formula:
Total number of outcomes = nCr (total number of children, number of children to be chosen)
In this case, the total number of children is 5 and we need to choose 2 children. Therefore, the total number of outcomes is 5C2 = 10.

Step 6: Calculating the probability:
Using the formula, we can calculate the probability as:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = (6 + 2) / 10
Probability = 8 / 10
Probability = 0.8 or 80%

Conclusion:
The probability of selecting at least one boy when two children are chosen randomly from a group of two boys and three girls is 0.8 or 80%.