Conditional Probability from a Table

Question

In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they have a sister?

Has a brother	Does not have a brother
Has a sister	2	6
Does not have a sister	7	8

Answer 1

There are 23 students in the group: 8 have a sister and 15 do not. 9 have a brother and 14 do not.

P(S)=8/23 and P(B)=9/23

P(S and B)=2/23

P(B|S)=P(B and S)/P(S)=(2/23)/(8/23)=1/4