This question was given to us as a bonus. No one in our class got it right, would you please send an answer and explain how you arrived at the answer. Thank you.
A health club with a membership of 650 people operates a running track and an indoor swimming pool. A survey of the membership indicates that 68% use the running track, 44% use the swimming pool, and 8% use neither. If a member is chosen at random, what is the prbability that the member uses:
a) Both the track and the pool?
b) Only the track?Hi Maria,
I would start by drawing a diagram to represent the memberships. The diagram I am going to draw is called a Venn Diagram.
Draw a rectangle to contain the 650 members. Inside the rectangle draw two circles. Inside the circle labeled T are the members who use the track and inside the circle labeled P are the members who use the pool.
8% of 650 is 52, so 52 members are not in either circle. Record the 52 on the diagram. Thus there are 650 - 52 = 598 members who either use the track or the pool.
68% of 650 is 442, hence there are 442 members inside the "T" circle.
You need to put numbers into the three remaining regions of the diagram, the region inside T but outside P, the region inside P but outside T and the region which is in both T and P. I have called these numbers a, b and c in the diagram below.
You know that
b + c = 286
a + b + c = 598
Once you know a, b and c you can find the probabilities.Cheers,