91Ó°ÊÓ

A restaurant offers the following limited lunch menu.$$ \begin{array}{|l|l|l|l|} \hline \text { Main Course } & \text { Vegetables } & \text { Beverages } & \text { Desserts } \\ \hline \text { Ham } & \text { Potatoes } & \text { Coffee } & \text { Cake } \\\ \hline \text { Chicken } & \text { Peas } & \text { Tea } & \text { Pie } \\ \hline \text { Fish } & \text { Green beans } & \text { Milk } & \text { Ice cream } \\ \hline \text { Beef } & & \text { Soda } & \\ \hline \end{array} $$ If one item is selected from each of the four groups, in how many ways can a meal be ordered? Describe two such orders.

Shoppers in a large shopping mall are categorized as male or female, over 30 or 30 and under, and cash or credit card shoppers. In how many ways can the shoppers be categorized?

A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of \(\$ 300,000\) if successful and a yearly loss of \(\$ 100,000\) otherwise. The probability of success is \(\frac{1}{2}\). If the second mall is selected, it is estimated that the yearly profit will be \(\$ 200,000\) if successful; otherwise, the annual loss will be \(\$ 60,000\). The probability of success at the second mall is \(\frac{3}{4}\). Which mall should be chosen in order to maximize the expected profit?

An oil company is considering two sites on which to drill, described as follows: Site A: Profit if oil is found: \(\$ 80\) million Loss if no oil is found: \(\$ 10\) million Probability of finding oil: \(0.2\) Site B: Profit if oil is found: \(\$ 120\) million Loss if no oil is found: \(\$ 18\) million Probability of finding oil: \(0.1\) Which site has the larger expected profit? By how much?

A committee of five people is to be formed from six lawyers and seven teachers. Find the probability that a. all are lawyers. b. none are lawyers.

A person can order a new car with a choice of six possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?

In Exercises 11-14, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

A city council consists of six Democrats and four Republicans. If a committee of three people is selected, find the probability of selecting one Democrat and two Republicans.

A parent-teacher committee consisting of four people is to be selected from fifteen parents and five teachers. Find the probability of selecting two parents and two teachers.

In Exercises 11-14, a single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time.