Question

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

There are 25 boys.
27 students choose football, of which 17 are girls.
18 students choose tennis.
24 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

P = 0,3749 or P = 37,49 %

Explanation:

17 girls play football 10 boys do ⇒ 27 students

24 girls running 3 boys do ⇒ 27 students

then 6 girls play tennis and 12 boys do ⇒ 18 students

Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )

P = P1 + P2

P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running

Probability of girl 47/72 = 0,6528

Probability of running is equal to 24/47 = 0,5106

Then the probability of girl running is equal to

P2 = 0,6528*0,5106 = 0,3333 or 33,33 %

P2 = 0,3333 or P2 = 33,33 %

Now we have 72 students 25 boys, then the probability of choosing a boy is = 25/72 = 0,3472

And the probability of running is 3/25 = 0,12

Then

P1 = 0,3472*0,12

P1 = 0,04166 and

P = P1 + P2

P = 0,04166 + 0,3333

P = 0,3749 or P = 37,49 %