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Ryan, Engineer

Category: Math Homework

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1.Your little sister loves visits from the Tooth Fairy. Suppose

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1.Your little sister loves visits from the Tooth Fairy. Suppose half the time the Tooth Fairy leaves $1 and half the time she leaves $0.60. What is the expected value of the Tooth Fairy's payoff?

2. A standard roulette wheel has 38 numbered slots for a small ball to land in: 36 are marked from 1 to 36, with half of those black and half red; two green slots are numbered 0 and 00. An allowable bet is to bet on either red or black. This bet is an even-money bet, which means if you win you receive twice what you bet. Many people think that betting black or red is a fair game. What is the expected value of betting $500 on red? Round the answer to the nearest integer.

3.You have three options for the evening. (a) You could watch some sitcoms on TV that you are certain to enjoy and that will provide you with a relative pleasure rating of 4. (b) You could go to a movie that is supposed to be good. You would enjoy the movie with probability 0.5; if you enjoy it, it will provide you with a relative pleasure rating of 11, but if you don't enjoy it, it will provide a negative rating of −2. (c) You could go on a date. With probability 0.3 you will experience a pleasure rating of 22, and with probability 0.7 the date will provide a negative rating of −2. What are the expected values of pleasure for these individual activities? TV expected value = Movie expected value = Date expected value =

4.Fair wheeling. A standard roulette wheel has 38 numbered spaces for a small ball to land in: 36 are marked from 1 to 36, half black and half red; 0 and 00 are green. You are at the roulette table and bet $500 on red 09. What payoff should you receive to make the game fair?Round the answer to the nearest integer. The payoff = $

5.Suppose a new vaccine that prevents the SARS (Severe Acute Respiratory Syndrome) virus is discovered. Each injection costs $25 and is expected to save 01 in(NNN) NNN-NNNNlives. What is the total cost per life saved for this vaccine?

6.You have high standards with respect to truth in advertising, particularly when it comes to hair color. One day at the laundromat, you meet an attractive blonde stranger named Chris and wonder if you should pursue a relationship. Unfortunately, you have the nagging belief that Chris's golden locks may have been the result of peroxide − presenting the specter of a dark (haired) future. However, you also know several facts about the incidence of dyed hair and about your ability to detect fraudulent follicles. You know that 70% of blonde people in the world are naturally blonde. You have done a personal survey and learned that you are 85% accurate in your ability to correctly categorize fake hair color as fake and real hair color as real. What is the probability that Chris's hair is fair and that your bleached beliefs were incorrect? Give your answer rounded to the nearest percent.

7. Each day U.S. commercial airlines log approximately 1.7 billion passenger miles with an average of 182 people killed per year. Suppose that if planes were made only 5 times safer, then airplane ticket prices would rise less than before, and thus only 1% of travelers who now fly would choose to drive instead. Assuming one automobile death per 100 million miles, what is the net result on lives lost per year if we make the planes safer? (round the answer to the nearest integer)

8. Suppose that at the beginning of party animal Sam Student's college career, he deposits $400 into a savings account that earns 3% interest per year, compounded annually. Exactly 10 years later, when Sam graduates, he closes the account. How much money does the bank give good old Sam? Round the answer to the nearest cent.

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