Given that a student has a brother, 57.14% is the probability that they also have a sister
Given that,
16 of the 30 students in the class have brothers, and 7 have sisters. There are 11 students that are sibling-free.
We have to find given that a student has a brother, what is the probability that they also have a sister.
Let x be the number of students having both brother and sister.
Brother only is 16-x
Sister only is 7-x
Brother only + sister only + both + neither = 30
(16-x) + (7-x) + x + 11 = 30
34 - x = 30
x = 4
The probability per the diagram is 4/7= 4/7
Per definition of conditional probability:
probability ( brother | sister) = probability ( brother AND sister) / probability ( sister)
= 4/7
4/7 = 0.5714 = 57.14%
Therefore, given that a student has a brother, 57.14% is the probability that they also have a sister
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