Ten people were asked if they have a brother or sister. this venn diagram shows the results. a person is randomly chosen from those shown in the venn diagram

Option D

means that of the 4 people who have a brother, 2 of them also have a sister

Step-by-step explanation:

Events are defined as follows.

Event A: The selected person has a sister

Event B: The selected person has a brother

The conditional probability of A given B is the probability that the selected person also has a sister since he has a brother.

This is:

We know that

P(B) is the probability that the selected person has a brother. Notice that there are 4 people who have a brother.

P(A and B) is the probability that the selected person has a brother and also a sister. Notice that there are 2 people who have a brother and a sister.

So means that of the 4 people who have a brother, 2 of them also have a sister