Question

In a class of 28 students, 11 have a brother and 9 have a sister. There are 2 students

Answer 1

Answer:

$\displaystyle P(A\mid B)=\frac{2}{11}$

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:

${\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}}}$

Where $P(A\cap B)$ 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:

$\displaystyle P(B)=\frac{11}{28}$

The probability that the student has a brother and a sister is:

$\displaystyle P(A\cap B)=\frac{2}{28}$

Thus, the conditional probability is:

${\displaystyle P(A\mid B)={\frac {\frac{2}{28}}{\frac{11}{28}}}}$

Simplifying:

$\mathbf{\displaystyle P(A\mid B)=\frac{2}{11}}$