Question

In a class 21 of students, 7 have a brother and 6 have a sister. There are 4 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?

Answer 1

Let x be the number of students having both brother and sister.

Brother only is 7-x
Sister only is 6-x


Brother only + sister only + both + neither = 21
(7-x) + (6-x) + x + 4= 21
-4 - x = 21
x = 17

Per definition of conditional probability:
prob( brother | sister) = prob ( brother AND sister) / prob ( sister)
17/6 = 2 5/6
17/6 = 2 5/6 = 25%