In a class of 27 students, 10 have a brother and 12 have a sister. There are 4 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?
To solve this problem, we can use the formula for conditional probability:
P(B|S) = P(B and S) / P(S)
where P(B|S) is the probability of having a brother given that the student has a sister, P(B and S) is the probability of having both a brother and a sister, and P(S) is the probability of having a sister.
We know that there are 4 students who have both a brother and a sister, so P(B and S) = 4/27. We also know that 12 students have a sister, so P(S) = 12/27.
To find P(B|S), we need to divide P(B and S) by P(S):
P(B|S) = (4/27) / (12/27)
Simplifying the fraction, we get:
P(B|S) = 4/12
Reducing the fraction, we get:
P(B|S) = 1/3
Therefore, the probability that a student who has a sister also has a brother is 1/3, or approximately 0.333.