Question

n 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 9
Does not have a sister 2 15

Answer 1

To find the probability that a student who does not have a sister has a brother, we need to look at the relevant data from the table.

From the table:

- Students who **do not have a sister** and **have a brother**: 2
- Students who **do not have a sister** and **do not have a brother**: 15

Now, we will calculate the total number of students who **do not have a sister**:

Total (do not have a sister) = 2 (have a brother) + 15 (do not have a brother) = 17

Now, we want the probability that a student who does not have a sister has a brother. This probability can be calculated as follows:

\[
P(\text{has a brother} \mid \text{does not have a sister}) = \frac{\text{Number of students who do not have a sister but have a brother}}{\text{Total number of students who do not have a sister}} = \frac{2}{17}
\]

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

\[
\frac{2}{17}
\]