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 brother given that they have a sister?

Explanation:

Step1: <Calculate the number of students who have a sister>

The number of students who have a sister is \(7 + 2=9\).

Step2: <Calculate the number of students who have a sister and a brother>

The number of students who have a sister and a brother is \(7\).

Step3: <Use the formula for conditional probability>

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of frequency (where \(n(A\cap B)\) is the number of elements in \(A\cap B\) and \(n(B)\) is the number of elements in \(B\)), \(P(\text{has a brother}|\text{has a sister})=\frac{n(\text{has a brother and a sister})}{n(\text{has a sister})}\). Substituting the values, we get \(\frac{7}{9}\).

Answer:

\(\frac{7}{9}\)