A film producer is evaluating a script by a new screenwriter. The producer knows that the probability of a play by a new screenwriter being a success is about 40 percent, and the probability of it being a failure is about 60 percent. The producer estimates that the profit will be $30 million if the play is a hit, but there will be a loss of $10 million if the play is a failure. The producer would like to hire a consultant to read the script and assess its probability of success/failure. The consultant has been able to correctly predict a successful play 70 percent of the time and correctly predict an unsuccessful play 80 percent of the time. What is the expected value of sample information? Group of answer choices $6 million $10 million $12 million $14 million Zero

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 $825,000 if successful and a yearly loss of $275,000 otherwise. The probability of success is 1/2. If the second mall is​ selected, it is estimated that the yearly profit will be $550,000 if​ successful; otherwise, the annual loss will be $165,000. The probability of success at the second mall is 3/4. What is the expected profit for both mall 1 and 2? Which mall should be chosen in order to maximize the expected​ profit?

College instructors who adopt this book are (we hope!) twice as likely to continue to use the book the following year as they are to drop it, whereas nonusers are four times as likely to remain nonusers the following year as they are to adopt this book    In the long term, what proportion of college instructors will be users of this book?

The gunner on the assault boat SS Minnie Chang fires six missiles at an attacking plane. Each has a 20% chance of being on target. If two or more shells find their mark, the plane will crash. At the same time, the pilot of the plane fires 10 surface-to-air rockets, each of which has a 0.05 chance of sinking the boat. If you want to live, would you rather be on the plane or on the boat?

A company is trying to decide if they should make a bid on a project that would generate 450,000 in profit. It will cost $100,000 to develop the bid and they will have a 35% chance of winning the contract. What is the expected net profit (project profit less bid development cost) associated with making the bid?

The​ (hypothetical) table below shows the relationship between the number of hours students work at​ part-time jobs each week and the number of years it takes then to graduate with an undergraduate degree. If a student works more than 5 hours per​ week, what is the probability that the student graduates in over 6​ years?

A man buys a racehorse for $25,000 and enters it in two races. He plans to sell the horse​ afterward, hoping to make a profit. If the horse wins both​ races, its value will jump to $105,000. If it wins one of the​ races, it will be worth $65,000. If it loses both​ races, it will be worth only $10,000. The man believes there is a 30​% chance that the horse will win the first race and a 35​% chance that it will win the second one. Assuming that the two races are independent​ events, find the​ man's expected profit.

Milan

You are an analyst for a consumer products company. You run a survey of 1000 customers and find that 80% of customers use gel packs for laundry detergent (the rest use liquid or powder) and 40% of customers use gel packs for their dishwasher detergent (the rest use liquid or powder). You also learn that twice as many customers use laundry detergent than dishwasher detergent.

Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $23,600 to the policy holder. Executives at Avicenna are considering offering these policies for $791 each. Suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. O Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. O Avicenna can expect to lose money from offering these policies.…