from a group of 2 boys and 3 girls, two children are selected at random. find the probability

1. both selected children are girls
2. the selected group consists of one boy and one girl
3. at least one boy is selected

Let the boys be b1 and b2 while the girls be g1, g2 and g3.

Sample space = (b1, b2), ​(b1, g1), ​(b1, g2), ​(b1, g3), ​​(b2, g1), ​, ​(b2, g2), ​, ​(b2, g3), (g1, g2), ​ (g1, g3), ​ (g2, g3).
Total outcome = 10
from this, 

1. 3/10
2. 6/10
3. 7/10

Thank you so much guyz

1. 6/10, 2. 4/10, 3. 2/10

can some1 explain the ans
 

7/10

probability both selected children are girls = 3/10

probability that the selected group consists of one boy and one girl = 3/5

probability that at least one boy is selected  = 7/10

Step-by-step explanation:

It is given that,from a group of 2 boys and 3 girls, two children are selected at random.

The total number of ways 2 children can be selected = 5C₂ = 10

Find probability both selected children are girls

Number of ways select 2 girls from 3 girls = 3C₂ = 3

probability both selected children are girls = 3/10

Find probability that the selected group consists of one boy and one girl

Number of ways the selected group consists of one boy and one girl = 2C₁*3C₁ = 6

probability that the selected group consists of one boy and one girl = 6/10 = 3/5

Find probability that at least one boy is selected

probability that at least one boy is selected = 1 - probability both selected children are girls

probability that at least one boy is selected  = 1- 3/10 = 7/10