Given a family with four children find the probability of th

Given a family with four children find the probability of the event. The oldest is a girl, given that there are at least two girls.

Solution

assuming 0 as girls and 1 as boys.

total combination of 4 children can be =2^4.=>16.

so 16 is the sample space.

required solution will be the combinations in which there are atleast 2 0\'s(assumning 0 as girls)including such in which first digit is also zero e.g 01110.

we see that there is total of 7 combinations possible of 16.

0000

0001

0010

0011

0100

0101

0110

so the probability is 7/16.