Question

99 students choose to attend one of three after school activities: football, tennis or running.

There are 61 boys.
19 students choose football, of which 5 are girls.
31 students choose tennis.
28 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.

Answer 1

Answer:
`(49)/(99)`

Explanation:

There are 61 boys --> 38 girls

A) 19 chose football: 5 are girls --> 14 are boys

B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis

C) 31 students chose tennis: 5 are girls --> 26 are boys.

D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.

`\large\boxed{\begin{array}cc&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}`

Total running = 21 boys + 28 girls = 49

Total students = 99

`\frac{\text{Total running}}{\text{Total students}}=\large\boxed{(49)/(99)}`