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)=(P(W\cap S))/(P(S))`

We can find from the table that:

`P(W\cap S)=(5)/(100)`

and

`P(S)=(25+5+5)/(100)=(35)/(100)`

Then, we can calculate our probability as:

`P(W|S)=(P(W\cap S))/(P(S))=((5)/(100))/((35)/(100))=(5)/(35)=(1)/(7)\approx0.14`

Answer: P(work | senior) = 0.14