Let's solve the problem step-by-step.
We need to find the probability that a student drives given that they are a senior. This probability is denoted as [tex]\( P(\text{drives} \mid \text{senior}) \)[/tex], which can be mathematically represented using the conditional probability formula:
[tex]\[
P(\text{drives} \mid \text{senior}) = \frac{P(\text{drives and senior})}{P(\text{senior})}
\][/tex]
First, we need to identify the required values from the given table.
1. Total number of seniors: This is the total number of students who are seniors.
- From the table, the total number of seniors is [tex]\( 35 \)[/tex].
2. Number of seniors who drive: This is the number of students who are seniors and also drive.
- From the table, the number of seniors who drive is [tex]\( 25 \)[/tex].
3. Probability of being a senior ( [tex]\( P(\text{senior}) \)[/tex] ): This is the proportion of students who are seniors out of the total number of students.
- The total number of students is [tex]\( 100 \)[/tex].
- Therefore, [tex]\( P(\text{senior}) = \frac{\text{Total number of seniors}}{\text{Total students}} = \frac{35}{100} \)[/tex].
4. Probability of driving and being a senior ( [tex]\( P(\text{drives and senior}) \)[/tex] ): This is the proportion of students who are both seniors and drive out of the total number of students.
- Therefore, [tex]\( P(\text{drives and senior}) = \frac{\text{Number of seniors who drive}}{\text{Total students}} = \frac{25}{100} \)[/tex].
To find [tex]\( P(\text{drives} \mid \text{senior}) \)[/tex]:
[tex]\[
P(\text{drives} \mid \text{senior}) = \frac{P(\text{drives and senior})}{P(\text{senior})} = \frac{\frac{25}{100}}{\frac{35}{100}} = \frac{25}{35}
\][/tex]
Simplifying [tex]\( \frac{25}{35} \)[/tex] gives us the final probability:
[tex]\[
P(\text{drives} \mid \text{senior}) = \frac{25}{35} = \frac{5}{7} \approx 0.714
\][/tex]
Hence, the probability that a student drives given that they are a senior is approximately:
[tex]\[
P(\text{drives} \mid \text{senior}) = 0.714
\][/tex]
Or as a fraction:
[tex]\[
P(\text{drives} \mid \text{senior}) = \frac{5}{7}
\][/tex]
