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Brown Pre-calculus, p. 634

PT: Expected Value, Sample Space

RW: Test Taking

On a multiple-choice test, a student is given five possible answers for each question.  The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer.  If the student has no idea of the correct answer for a particular question and merely guesses, what is the student’s expected gain or loss on the question?

Suppose also that on one of the questions you can eliminate two of the five answers as being wrong.  If you guess at one of the remaining three answers, what is your expected gain or loss on the question?

Brown Pre-calculus, p. 634

PT: Expected Value

RW: Farming/Reading a Table

A dairy farmer estimates for the next year the farm’s cows will produce about 25,000 gallons of milk.  Because of variation in the market price of milk and cost of feeding the cows, the profit per gallon may vary with the probabilities given in the table below.  Estimate the profit on the 25,000 gallons.

Brown Pre-calculus, p. 634

PT: Expected Value

RW: Life Insurance

At many airports, a person can pay only $1.00 for a $100,000 life insurance policy covering the duration of the flight.  In other words, the insurance company pays $100,000 if the insured person dies from a possible flight crash; otherwise the company gains $1.00 (before expenses).  Suppose that past records indicate 0.45 deaths per million passengers.  How much can the company expect to gain on one policy?  On 100,000 policies?

Brown Pre-calculus, p. 635

PT: Expected Value

RW: Bidding on jobs

A construction company wants to submit a bid for remodeling a school.  The research and planning needed to make the bid cost $4000.  If the bid were accepted, the company would make $26,000.  Would you advise the company to spend the $4000 if the bid has only 20% probability of being accepted?  Explain your reasoning.

Brown Pre-calculus, p. 635

PT: Expected Value

RW: Consumer Economics

Suppose the warranty period on your family’s new television is about to expire and you are debating about whether to buy a one-year maintenance contract for $35.  If you buy the contract, all repairs for one year are free.  Consumer information shows that 12% of the televisions like yours require an annual repair that costs $140 on the average.  Would you advise buying the maintenance contract?  Explain your reasoning.

Key to Problem Bank: