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 terms of counts, if $n(A\cap B)$ is the number of elements in $A\cap B$ and $n(B)$ is the number of elements in $B$, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, event $A$ is "has a sister" and event $B$ is "has a brother".

Step2: Identify $n(A\cap B)$ and $n(B)$

The number of students who have a sister and a brother, $n(A\cap B) = 3$. The number of students who have a brother, $n(B)=3 + 4=7$.

Step3: Calculate the conditional probability

$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{3}{7}$.

Answer:

$\frac{3}{7}$