We have to find the probability P(work | senior).
This means the probability that the student works given that is a senior.
This probability can be calculated as:
[tex]P(W|S)=\frac{P(W\cap S)}{P(S)}[/tex]
We can find from the table that:
[tex]P(W\cap S)=\frac{5}{100}[/tex]
and
[tex]P(S)=\frac{25+5+5}{100}=\frac{35}{100}[/tex]
Then, we can calculate our probability as:
[tex]P(W|S)=\frac{P(W\cap S)}{P(S)}=\frac{\frac{5}{100}}{\frac{35}{100}}=\frac{5}{35}=\frac{1}{7}\approx0.14[/tex]
Answer: P(work | senior) = 0.14
