Question: Ten percent of the families in a town have no children, twenty percent have one child forty percent have two children, twenty percent have three, and ten percent have four. Assume each child in family is equally likely to be a body or a girl, independently of all the others. A family is picked at random from this town. Given that there is at least one boy in the family, what is the chance that there is also at least one girl?
In a large population, the distribution of the number of children per family is as follows:
|
Number of children n
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Proportion families with n children
|
0.15
|
0.2
|
0.3
|
0.2
|
0.1
|
0.05
|
Assume that each child in a family is boy or a girl with probability 1/2, independently
a) If a family is picked at random, what is the chance that it contains exactly tow girls?
b) If a child is picked at random from the children of this population, whit is the chance that the child comes from a family with exactly two girls?