Question

The following two-way table describes student'safter school activities. Find the probability that arandomly selected student works, given that it's asenior.GradeSportsMusic/DramaWorkSophomore2073Junior20132Senior2555P( Work | Senior) = [?]Round to the nearest hundredth.

Answer 1

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:

$P(W|S)=\frac{P(W\cap S)}{P(S)}$

We can find from the table that:

$P(W\cap S)=\frac{5}{100}$

and

$P(S)=\frac{25+5+5}{100}=\frac{35}{100}$

Then, we can calculate our probability as:

$P(W|S)=\frac{P(W\cap S)}{P(S)}=\frac{\frac{5}{100}}{\frac{35}{100}}=\frac{5}{35}=\frac{1}{7}\approx0.14$

Answer: P(work | senior) = 0.14