Chapter 11.1, Problem 7E

Use the information in Exercise 3 to predict the market shares of Silver’s gym, Fitness Lab, and ThinNFit at the second following purchase.

In exercises 1-4, (a) write the given data in probability form, and find their complementary probabilities. (b) draw a tree diagram that shows the given information, and (c) use the tree diagram to predict market share at the first following purchase, as done in Example 1.

3. Forty-eight percent of the health club members in Metropolis belong to Silver’s Gym, 37% belong to Fitness Lab, and the balance belong to ThinNFit. An extensive survey of gym members in Metropolis indicates that 71% of the current members of Silver’s will continue their annual membership when it expires, 12% will quit and join and join Fitness Lab, and the rest will go to ThinNFit. Fitness Lab has not kept its equipment in good shape, and as a result 32% of its members will dedect to Silvers and 34% will go to ThinNFit.96% plan on renewing their annual membership, with half of the rest planning to move to Silver’s and half to Fitness Lab.