Answer: Option D
[tex]P (A | B) = 0.5[/tex] 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:
[tex]P(A|B)=\frac{P(A\ and B)}{P(B)}[/tex]
[tex]P(A|B)=\frac{Number\ of\ elements\ in\ A\ and\ B}{Number\ of\ elements\ in\ B}[/tex]
We know that [tex]P(A|B)=0.5[/tex]
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 [tex]P(A | B) =0.5[/tex] means that of the 4 people who have a brother, 2 of them also have a sister
