At the local sports academy, everybody plays netball or tennis. Given that half the tennis players also play netball and one-third of the netballers also play tennis, what is the probability that a randomly chosen person at the academy plays both?

Answer 1

Draw a Venn diagram with a T (tennis) circle intersecting a N (netball) circle
It says that half the tennis players also play netball, so place x in the intersection and the
part of T outside the intersection.
It says one-third of the netballers also play tennis, so place (1/3)y in the intersection and (2/3)y in the N circle outside the intersection, but
x = (1/3)y
The total players is x + y = (1/3)y + y = (4/3)y
those playing both is (1/3)y
prob(both) = (1/3)y / ((4/3)y) = 1/4