In a family with 8 children, excluding multiple births, what is the probability of having 8 girls?
Assume that a girl is as likely as a boy at each birth.
Solution:-
Let the sample space S be of all possible permutations of girls and boys for 8 children.
There are 2 possibilities for each of 8 children. Thus using the multiplication principle, the total number of permutation will be 28. Therefore, the number of element is S is
n(S) = 28 = 256
Let the event E be the set of all element that correspond to the outcome “having 8 girls”.
Since there is only one way that 8 girls out of 8 children can occur, there is only 1 element in the E.
n(E) = 1
Thus, the probability of having 8 girls is
P(E) = 
= 