1. A game is played using one die
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game’s expected value? What does this value mean?

2. A construction company is planning to bid on a building contract
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 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.

3. 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.

4. 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 Determine the company’s expected gain per policy. .

5. A store specializing in mountain bikes is to open in one of two malls
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 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 3/4 . Which mall should be chosen in order to maximize the expected profit? .

6. 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?

7. Example: 2
The College Board website provides much information for students, parents, and professionals with respect to the many aspects involved in Advanced Placement (AP) courses and exams. One particular annual report provides the percent of students who obtain each of the possible AP grades (1 through 5). The 2008 grade distribution for all subjects was as follows:
AP Grade Percent
a. ) Express this distribution as a discrete probability distribution.
b. ) Find the mean and standard deviation of the AP exam scores for 2008.

8. Properties of the Binomial Probability Distributions
1- The experiment consists of a sequence of n identical trials
2- Two outcomes (SUCCESS and FAILURE ) are possible on each trial
3- The probability of success, denoted by p, does not change from trial to trial. Consequently, the probability of failure, denoted by q and equals to 1-p , does not change from trial to trial
4- The trials are independent.

9. Example :4
The Heart Association claims that only 10% of adults over 30 can pass the minimum requirements of Fitness Test. Suppose four adults are randomly selected and each is given the fitness test.
Use the formula for a binomial random variable to find the probability distribution of x, where x is the number of adults who pass the fitness test. Graph the distribution.