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

2/(2+6+7+8) = 2/23 = about 8.7% probability

only 2 have both a brother and sister

there are 23 total students

2 out of 23 is about .087 = 8.7%

but for a student who has a sister

the probability is 2/(2+6) = 2/8= 1/4 = 25%

Answer 2

Adjusting for mis-positioned column headings, 8 total have a sister (2 + 6), of whom 2 have brothers. Conditional probability P(B|S) is 2/8 = 1/4 or 25%.