Problem 1MS: What do you expect? How do you compute an expected value? Problem 2MS: The average bite. Your little sister loves visits from the Tooth Fairy. Suppose half the time the... Problem 3MS: A tooth for a tooth? Suppose your cousins Tooth Fairy leaves $1 one-third of the time, $0.50... Problem 4MS: Spinning wheel. Suppose the spinner shown is balanced, so the arrow is equally likely to land in any... Problem 5MS: Fair game. What does it mean for a game to be fair? Problem 6MS: Cross on the green (S). A standard roulette wheel has 38 numbered slots for a small ball to land in:... Problem 7MS: In the red. Given the bet from Mindscape 6, what should the payoff be if the game is to be a fair... Problem 8MS: Free Lotto. For several years in Massachusetts, the lottery commission would mail residents coupons... Problem 9MS: Bank value. What is the expected value of keeping $100 in a bank for one year if the bank pays 3%... Problem 11MS: Value of money. In Newcombs Paradox, first suppose that you have no money and have not eaten in two... Problem 12MS: Die roll. What is the expected value of each of the outcomes (1,2,3,4,5, or 6) of rolling a fair... Problem 13MS: Dice roll (ExH). What is the expected value of each of the outcomes (2,3,4,5,…,12) of rolling two... Problem 14MS: Fair is foul. Someone has a weighted coin that lands heads up with probability 2/3 and tails up with... Problem 15MS: Foul is fair (S). Someone has a weighted coin that lands heads up with probability 2/3 and tails up... Problem 16MS: Cycle cycle (H). You live in an area where the probability that ones bicycle is stolen is 0.2. You... Problem 17MS: Whats your pleasure? You have three options for the evening. (1) You could watch some sitcoms on TV... Problem 18MS: Roulette expectation. A standard roulette wheel has 38 numbered spaces for a small ball to land in:... Problem 19MS: Fair wheeling. You are at the roulette table and bet $100 on red 9. What payoff should you received... Problem 20MS: High rolling (H). Here is a die game you play against a casino. You roll a fair die. If you roll 1,... Problem 21MS: Fair rolling. Suppose you are considering the game described in Mindscape 20. How much would you... Problem 22MS: Spinning wheel. You pay $5, pick one of the four spinners below, and spin that spinner. Each spinner... Problem 23MS: Dice (ExH). You place a bet and then roll two fair dice. If you roll a sum of 7 or 11, you receive... Problem 24MS: Uncoverable bases. Show by a specific example how it is possible to lose at the lottery even if the... Problem 25MS: Under the cap. A national soda company runs a promotional contest. Under the cap of one in a million... Problem 26MS: Two coins in a fountain. You pay Si for two coins to toss in a fountain and see how they land. If... Problem 27MS: Three coins in a fountain. You pay $5 for three coins to toss in a fountain and see how they land.... Problem 28MS: Insure (S). You own a $9000 car and a $850 mountain bike. The probability that your car will be... Problem 29MS: Get a job (H). You search for a job. Three companies are interested in you, and you will receive at... Problem 30MS: Take this job and... Given the employment scenario described in the previous Mindscape, suppose that... Problem 31MS: Book value. Refer back to our analysis of the expected value of reading this book (pages 766–767).... Problem 32MS: In search of... A group of deep-sea divers approaches you with a proposition. They are 60% certain... Problem 33MS: Solid gold. There is a 50% chance that the price of gold will go up $25 an ounce; a 20% chance that... Problem 34MS: Four out of five. In Newcombs Paradox, suppose that the psychologist predicts the choice of the... Problem 35MS: Chevalier de Méré. Suppose that the Chevalier de Mëré bets 1000 euros that a 6 will appear at... Problem 36MS: The St. Petersburg paradox. Here is an interesting game: You pay a certain amount of money to play.... Problem 37MS: Coin or god. In Newcombs Paradox, first suppose that the psychologist just flips a coin to determine... Problem 38MS: An investment. You wish to invest $1000, and you have two choices. One is a sure thing, and you will... Problem 39MS: Pap test (H). Assume that the insurance value of a life is $1,200,000. Suppose Pap smear tests will... Problem 40MS Problem 45MS: Spin to win. To play a certain carnival game, you spin a wheel to obtain one of the nine equally... Problem 46MS: Spinner winner. To play a different carnival game, you spin a wheel to obtain one of the 30 equally... Problem 47MS: Insurance wagering (H). From the point of view of an insurance company, the expected value of an... Problem 48MS: Probable cause. Continuing the scenario from the previous Mindscape, suppose the cost of the... Problem 49MS: The bicycle thief. Some entrepreneurial classmates start a business selling insurance for bicycle... format_list_bulleted