Question

from all families with three children and family is selected at random and then a child is selected from it at random and is found to be a girl what is the probability that she came from a family with two girls and one boy( assume that each child is a boy or a girl with the probability one by two independently of one another.)​

Answer 1

Answer:

It is customary to say that the probability of getting a boy is

1

2

. It may come as a surprise, but as we are not living in an ideal world, this is only an approximation. Data from the US and Scandinavia show that the true figure is more like 51% for a boy and 49% for a girl.

In addition statistics show that the probability of the child having a specific sex is correlated with the sex of the previous children. If the family for instance already have 2 boys, the probability of the third child being a boy is a little more than 52%. To get a more precise figure we should really take these facts into account.

But as a rough guide a probability of

1

2

for a boy and a girl and that the sex of one child is independent of the sex of the other children would be close enough.

As the calculation is already shown in another answer, I won't repeat it here, only give the rough answers:

P(A)=P(all boys)

≈

1

8

P(B)=P(all boys or all girls)

≈

1

4

P(C)=P(2 boys or 2 girls)

≈

3

4

P(D)=P(at least 1 of each gender)

≈

3

4