Question

a teacher asked students in his class if they had any brothers or sisters. the results are shown at the right. what is the chance of randomly selecting a someone from this group with a brother given that they have a sister

Explanation:

Step1: Calculate the number of students with a sister

The number of students with a sister is the sum of those who have only sisters and those who have both brothers and sisters. So, \(12 + 5=17\).

Step2: Calculate the number of students with both a brother and a sister

The number of students with both a brother and a sister is \(5\).

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 (counts), if \(A\) is the event of having a brother and \(B\) is the event of having a sister, then the probability of having a brother given that they have a sister is \(\frac{\text{Number of students with both}}{\text{Number of students with a sister}}\). So, \(P=\frac{5}{17}\).

Answer:

\(\frac{5}{17}\)