91Ó°ÊÓ

Seven performers, A, B, C, D, E, F, and G, are to appear in a fund raiser. The order of performance is determined by random selection. Find the probability that a. D will perform first. b. E will perform sixth and \(B\) will perform last. c. They will perform in the following order: C, D, B, A, G, \(\mathrm{F}, \mathrm{E}\). d. \(F\) or \(G\) will perform first.

An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is \(\$ 10,000\). The probability of being awarded the bid is \(0.1\), and anticipated profits are \(\$ 100,000\), resulting in a possible gain of this amount minus the \(\$ 10,000\) cost for plans and a model. What is the expected value in this situation? Describe what this value means.

A group consists of four men and five women. Three people are selected to attend a conference. a. In how many ways can three people be selected from this group of nine? b. In how many ways can three women be selected from the five women? c. Find the probability that the selected group will consist of all women.

A construction company is planning to bid on a building contract. The bid costs the company \(\$ 1500\). The probability that the bid is accepted is \(\frac{1}{5}\). If the bid is accepted, the company will make \(\$ 40,000\) minus the cost of the bid. Find the expected value in this situation. Describe what this value means.

A political discussion group consists of five Democrats and six Republicans. Four people are selected to attend a conference. a. In how many ways can four people be selected from this group of eleven? b. In how many ways can four Republicans be selected from the six Republicans? c. Find the probability that the selected group will consist of all Republicans.

An ice cream store sells two drinks (sodas or milk shakes), in four sizes (small, medium, large, or jumbo), and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

Mega Millions is a multi state lottery played in most U.S. states. As of this writing, the top cash prize was \(\$ 656\) million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 7-10. Express all probabilities as fractions. A player wins the jackpot by matching all five numbers drawn from the white balls ( 1 through 56 ) and matching the number on the gold Mega Ball \({ }^{\circledR}\) (1 through 46). What is the probability of winning the jackpot?

It is estimated that there are 27 deaths for every 10 million people who use airplanes. A company that sells flight insurance provides \(\$ 100,000\) in case of death in a plane crash. A policy can be purchased for \(\$ 1\). Calculate the expected value and thereby determine how much the insurance company can make over the long run for each policy that it sells.

A 25 -year-old can purchase a one-year life insurance policy for \(\$ 10,000\) at a cost of \(\$ 100\). Past history indicates that the probability of a person dying at age 25 is \(0.002\). Determine the company's expected gain per policy.

A pizza can be ordered with three choices of size (small, medium, or large), four choices of crust (thin, thick, crispy, or regular), and six choices of toppings (ground beef, sausage, pepperoni, bacon, mushrooms, or onions). How many onetopping pizzas can be ordered?