in a class of 23 students, 7 have a brother and 5 have a sister. there are 2 students who have a brother and…

Explanation:

Step1: Identify relevant numbers

Let $A$ be the event of having a brother and $B$ be the event of having a sister. We know $n(A)=7$, $n(A\cap B) = 2$, and total students $n = 23$. We want to find $P(B|A)$.

Step2: Apply conditional - probability formula

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$. Since $P(A)=\frac{n(A)}{n}$ and $P(A\cap B)=\frac{n(A\cap B)}{n}$, then $P(B|A)=\frac{n(A\cap B)}{n(A)}$.

Step3: Calculate the probability

Substitute $n(A\cap B) = 2$ and $n(A)=7$ into the formula. So $P(B|A)=\frac{2}{7}$.

Answer:

$\frac{2}{7}$