Problem 3 Tom has one sibling What is the probability that h

Problem 3. Tom has one sibling. What is the probability that he has a sister ??

Thanks !!

Solution

Hi..

If this question had asked the probability of a pair of siblings having a girl if one of the siblings is known to be a boy then the answer would be 2/3. This is because the possibilities are BB,BG, or GB.

However, this question specifically points out one of the siblings.

Now Tom can be the older sibling or the younger sibling. If the older, he can have a younger brother or a younger sister. If he is the younger sibling, he can have an older brother or an older sister. Let T be Tom, B be a brother and S be a sister. The order of the pairs is the birth order:

The possibilities are (T,B),(T,S),(B,T),(S,T). There are 4 cases, two of which have a female sibling, so the correct answer is indeed 1/2.

The reason for the difference is that there are now 2 different cases of two boys. If M is male and F female, we do not have MM,MF,FM,FF. Instead we have Mm,mM,MF,FM where M,m and m,M are the different cases of whether Tom is older or younger.