Chapter 11.1, Problem 4E

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.

Smallville has three Chinese restaurants: Asia Gardens, Chef Chao’s, and Chung King Village. Currently, Asia Gardens gets $14\%$ of the business, Chef Chao’s gets $33\%$, and Chung King Village gets the balance. Chung King Village recently mailed a coupon to all residents of Smallville offering two dinners for the price of one. As a result, $67\%$ of those who normally eat at Asia Gardens plan on trying Chung King Village the next time they eat Chinese food, and $59\%$ of those who normally eat at Chef Chao’s plan on trying Chung King Village. Also, all of Chung King Village’s regular customers will return to take advantage of the special, and $30\%$ of the people who normally eat at Asia Gardens will eat there the next time they eat Chinese food because of its convenient location. Chef Chao’s has a new chef who isn’t doing very well, and as a result, only $15\%$ of the people who normally eat there are planning to return next time.