Question

The following two-way table describes student's

after school activities. Find the probability that a
randomly selected student works, given that it's a
senior.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P( Work | Senior) = [?]
Round to the nearest hundredth.

Answer 1

14%

Explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer 2

`P(Work | Senior) = 0.14`

Explanation:

Given

The attached table

Required

`P(Work | Senior)`

This is calculated using:

`P(Work | Senior) = (P(Work \ n\ Senior))/(P(Senior))`

This gives:

`P(Work | Senior) = (n(Work \ n\ Senior))/(n(Senior))`

From the table:

`n(Work \ n\ Senior) = 5`

`n(Senior) = 25 + 5+ 5 = 35`

So:

`P(Work | Senior) = (5)/(35)`

`P(Work | Senior) = 0.14`