Question

in a class of students, the following data table summarizes how many students have a brother or a sister. what is the probability that a student has a sister given that they have a brother?

Explanation:

Step1: Calculate the number of students who have a brother

The number of students who have a brother is the sum of those who have a brother and a sister ($11$) and those who have a brother but no sister ($5$). So, $11 + 5=16$.

Step2: Calculate the probability

The probability that a student has a sister given that they have a brother is calculated using the formula for conditional probability $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, $A$ is the event of having a sister and $B$ is the event of having a brother. $n(A\cap B) = 11$ (students with both brother and sister) and $n(B)=16$ (students with a brother). So the probability is $\frac{11}{16}$.

Answer:

$\frac{11}{16}$