Question

In a class of 30 students, 16 have a brother and 7 have a sister. There are 11 students who do not have any siblings. What is the probability that a student has a sister given that they have a brother?

Answer 1

To find the probability that a student has a sister given that they have a brother, we use conditional probability. Based on the given information, the probability is 43.75%.

Step-by-step explanation:

To find the probability that a student has a sister given that they have a brother, we need to use conditional probability. The conditional probability formula is:

P(A|B) = P(A and B) / P(B)

In this case, A represents having a sister and B represents having a brother. From the given information, we know that there are 16 students who have a brother, 7 students who have a sister, and 11 students who do not have any siblings.

So, P(B) = 16/30 and P(A and B) = 7/30.

Substituting these values into the conditional probability formula, we get:
P(A|B) = (7/30) / (16/30) = 7/16 = 0.4375 = 43.75%