Question

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

Answer 1

Answer: Option D

`P (A | B) = 0.5` means that of the 4 people who have a brother, 2 of them also have a sister

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:

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

`P(A|B)=(Number\ of\ elements\ in\ A\ and\ B)/(Number\ of\ elements\ in\ B)`

We know that
`P(A|B)=0.5`

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
`P(A | B) =0.5` means that of the 4 people who have a brother, 2 of them also have a sister