Question

the two-way table displays student involvement.
follow the steps to find the probability a student is in sports, given that they are a senior.
\\(p(\text{senior}) = ?\\%\\)
\\(p(\text{senior and sports}) = \quad \\%\\)
\\(p(\text{sports} \mid \text{senior}) = \frac{p(\text{sports and senior})}{p(\text{senior})} = \quad \\%\\)
round your answer to the nearest whole percent.

Explanation:

Identify the given values from the table

We extract the relevant frequencies from the two-way table:

• Total number of students: \(N = 100\)
• Total number of seniors: \(n(\text{senior}) = 35\)
• Number of seniors in sports: \(n(\text{senior and sports}) = 25\)

Calculate the probability of being a senior

Using Theoretical Probability:

$$ P(\text{senior}) = \frac{n(\text{senior})}{N} = \frac{35}{100} = 35\% $$

Calculate the joint probability of being a senior in sports

Using Theoretical Probability:

$$ P(\text{senior and sports}) = \frac{n(\text{senior and sports})}{N} = \frac{25}{100} = 25\% $$

Calculate the conditional probability

Apply the conditional probability formula:

$$ P(\text{sports} \mid \text{senior}) = \frac{P(\text{sports and senior})}{P(\text{senior})} = \frac{25\%}{35\%} = \frac{25}{35} \approx 0.7143 $$

Rounding to the nearest whole percent gives \(71\%\).

Answer:

Follow the steps to find the probability a student is in sports, given that they are a senior.

\(P(\text{senior}) =\) <blank>\(35\)</blank>\(\%\)

\(P(\text{senior and sports}) =\) <blank>\(25\)</blank>\(\%\)

\(P(\text{sports} \mid \text{senior}) = \frac{P(\text{sports and senior})}{P(\text{senior})} =\) <blank>\(71\)</blank>\(\%\)

Round your answer to the nearest whole percent.