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.
+526 Let n(F) choose football, n(T) in tennis, n(R) in running, n(B) boys and n(G) girls
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
\(P(R) = {20\over 115} = {4\over 23}=0.17\)
