Answer:
7/10
Step-by-step explanation:
For a person to use at least two of the facilities means they can use the three facilities as well.
Let n(U) be the total people in the sport centre = 100
n(G) be people that uses gym = 67
n(S) be people that uses swimming pool = 62
n(T) be people that uses track = 56
n(GnP) be gym and pool = 38
n(PnT) be people that use the pool and the track = 31
n(GnT) be people that use the gym and the track = 33
n(GnPnT) be people that use all three facilities = 16
People that uses gym and pool only = n(GnP) - n(GnPnT)
= 38-16
= 22
People that uses pool and track only = n(PnT) - n(GnPnT)
= 31-16
= 15
People that uses gym and track only = n(GnT) - n(GnPnT)
= 33-16
= 17
Total people that uses at least 2 facilities = 16+22+15+17 = 70
Probability that this person uses at least 2 facilities = Total people that uses at least 2 facilities/Total people in the sport centre
Probability that this person uses at least 2 facilities = 70/100 = 7/10
