in a class of students, the following data table summarizes how many students have a brother or a sister…

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event that a student has a brother and $B$ be the event that a student has a sister. Then $P(A\cap B)$ is the probability that a student has both a brother and a sister, and $P(B)$ is the probability that a student has a sister.

Step2: Calculate $P(A\cap B)$ and $P(B)$

The number of students who have both a brother and a sister is $n(A\cap B) = 3$. The number of students who have a sister is $n(B)=3 + 20=23$. The probability $P(A\cap B)=\frac{3}{3 + 20+2 + 4}=\frac{3}{29}$, and $P(B)=\frac{3 + 20}{3 + 20+2 + 4}=\frac{23}{29}$.

Step3: Calculate the conditional probability

Using the formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$, substituting the values we found: $P(A|B)=\frac{\frac{3}{29}}{\frac{23}{29}}=\frac{3}{23}$.

Answer:

$\frac{3}{23}$