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 who does not have a sister has a brother?
Has a brother Does not have a brother
Has a sister 4 7
Does not have a sister 5 11
Answer
Attempt 1 out of 2

Answer 1

To find the probability that a student who does not have a sister has a brother, we can refer to the relevant values in the data table.

From the table, we have:

- Students who **do not have a sister and have a brother**: 5
- Students who **do not have a sister and do not have a brother**: 11

First, we need to find the total number of students who **do not have a sister**:

\[
\text{Total who do not have a sister} = \text{(those who do not have a sister and have a brother)} + \text{(those who do not have a sister and do not have a brother)}
\]
\[
\text{Total who do not have a sister} = 5 + 11 = 16
\]

Now we can determine the probability that a student who does not have a sister has a brother:

\[
P(\text{Has a brother | Does not have a sister}) = \frac{\text{Number of students who do not have a sister and have a brother}}{\text{Total number of students who do not have a sister}}
\]
\[
P(\text{Has a brother | Does not have a sister}) = \frac{5}{16}
\]

Therefore, the probability that a student who does not have a sister has a brother is:

\[
\boxed{\frac{5}{16}}
\]