Answer:
[tex]\displaystyle P(A\mid B)=\frac{2}{11}[/tex]
Step-by-step explanation:
Conditional Probability
Is a measure of the probability of the occurrence of an event, given that another event has already occurred. If event B has occurred, then the probability that event A occurs is given by:
[tex]{\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}}}[/tex]
Where [tex]P(A\cap B)[/tex] is the probability that both events occur and P(B) is the probability that B occurs.
Let's define events A and B for the question. There are 11 students that have a brother and 9 that have a sister. Two of those students have a brother and a sister.
We are given the fact that the selected student has a brother: this is the event that has already occurred, thus:
B = A student has a brother
A = A student has a sister
The probability that a student has a brother is:
[tex]\displaystyle P(B)=\frac{11}{28}[/tex]
The probability that the student has a brother and a sister is:
[tex]\displaystyle P(A\cap B)=\frac{2}{28}[/tex]
Thus, the conditional probability is:
[tex]{\displaystyle P(A\mid B)={\frac {\frac{2}{28}}{\frac{11}{28}}}}[/tex]
Simplifying:
[tex]\mathbf{\displaystyle P(A\mid B)=\frac{2}{11}}[/tex]
