Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are…

Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won two games. The first game is played in New York, the second game … Continue reading "Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are…"

A manufacturing company is trying to decide whether to sign a contract with the government to…

A manufacturing company is trying to decide whether to sign a contract with the government to deliver an instrument to the government no later than eight weeks from now. Due to various uncertainties, the company isn’t sure when it will be able to deliver the instrument. Also, when the instrument is delivered, there is a … Continue reading "A manufacturing company is trying to decide whether to sign a contract with the government to…"

Have you ever watched the odds at a horse race? You might hear that the odds against a given…

Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being converted to probabilities, typically add to something greater than one. Why … Continue reading "Have you ever watched the odds at a horse race? You might hear that the odds against a given…"

Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are…

Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won two games. The first game is played in New York, the second game … Continue reading "Suppose the New York Yankees and Philadelphia Phillies (two Major League Baseball teams) are…"

The application at the beginning of this chapter describes the campaign McDonald’s used several…

The application at the beginning of this chapter describes the campaign McDonald’s used several years ago, where customers could win various prizes. a. Verify the figures that are given in the description. That is, argue why there are 10 winning outcomes and 120 total outcomes. b. Suppose McDonald’s had designed the cards so that each … Continue reading "The application at the beginning of this chapter describes the campaign McDonald’s used several…"

A manufacturing company is trying to decide whether to sign a contract with the government to…

A manufacturing company is trying to decide whether to sign a contract with the government to deliver an instrument to the government no later than eight weeks from now. Due to various uncertainties, the company isn’t sure when it will be able to deliver the instrument. Also, when the instrument is delivered, there is a … Continue reading "A manufacturing company is trying to decide whether to sign a contract with the government to…"

Have you ever watched the odds at a horse race? You might hear that the odds against a given…

Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being converted to probabilities, typically add to something greater than one. Why … Continue reading "Have you ever watched the odds at a horse race? You might hear that the odds against a given…"

Choose at least one uncertain quantity of interest to you. For example, you might choose the…

Choose at least one uncertain quantity of interest to you. For example, you might choose the highest price of gas between now and the end of the year, the highest point the Dow Jones Industrial Average will reach between now and the end of the year, the number of majors Tiger Woods will win in … Continue reading "Choose at least one uncertain quantity of interest to you. For example, you might choose the…"

An investor has invested in nine different investments. The dollar returns on the different…

An investor has invested in nine different investments. The dollar returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $50,000 and standard deviation $10,000. a. There is a 1% chance that the total return on the nine investments is less than what value? b. What is the … Continue reading "An investor has invested in nine different investments. The dollar returns on the different…"