115 students choose to attend one of three after school activities: football, tennis or running. There are 54 boys.

52 students choose football, of which 25 are girls.

43 students choose tennis.

10 girls choose running.

A student is selected at random.

What is the probability this student chose running?

Give your answer in its simplest form.

Guest Jun 13, 2021

#1**+2 **

Let n(F) choose football, n(T) in tennis, n(R) in running, n(B) boys and n(G) girls

- n(F∪T∪R) = 115
- n(B) = 54 ⇒n(G) = 115 - 54 = 61
- n(F) = 52 ⇒n(F∩G) = 25 so n(F∩B) = 52 - 25 = 27
- n(T) = 43
- n(R∩G) = 10

**No. of girls in tennis**

n(T∩G) = n(G) - [n(F∩G) + n(R∩G)] = 61 - (25 + 10) = 26

**No. of boys in tennis**

n(T∩B) = n(T) - n(T∩G) = 43 - 26 = 17

∴ **Remaining no. of boys in running**

n(R∩B) = n(B) - [n(F∩B) - n(T∩B)] = 54 - (27 + 17) = 10

⇒n(R) = n(R∩G) + n(R∩B) = 10 + 10 = 20

Probability of choosing running

\(P(R) = {20\over 115} = {4\over 23}=0.17\)

amygdaleon305 Jun 14, 2021