# Question: In Monopoly dice are used to determine which player gets

In Monopoly, dice are used to determine which player gets to move first. Suppose there are two players in the game. Each player rolls a die and the player with the higher number gets to move first. If the numbers are the same, the players roll again.

a. Using the sample space {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), . . . (6, 5), (6, 6)} of the 36 equally likely outcomes for the two dice, show that the probability distribution for the maximum of the two numbers is as shown in the table. For each outcome in the sample space, indicate the value of X assigned to that outcome.

Probability Distribution of X = Maximum

Number for Rolls of Two Dice

x P( x )

1...... 1/36

2...... 3/36

3...... 5/36

4...... 7/36

5...... 9/36

6...... 11/36

b. Show that the two conditions in the definition of a probability distribution are satisfied.

a. Using the sample space {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), . . . (6, 5), (6, 6)} of the 36 equally likely outcomes for the two dice, show that the probability distribution for the maximum of the two numbers is as shown in the table. For each outcome in the sample space, indicate the value of X assigned to that outcome.

Probability Distribution of X = Maximum

Number for Rolls of Two Dice

x P( x )

1...... 1/36

2...... 3/36

3...... 5/36

4...... 7/36

5...... 9/36

6...... 11/36

b. Show that the two conditions in the definition of a probability distribution are satisfied.

## Answer to relevant Questions

a. For the normal distribution shown below, find the z -score. b. Find the value of z (rounding to two decimal places) for right-tail probabilities of (i) 0.05 and (ii) 0.005. An energy study in Gainesville, Florida, found that in March 2006, household use of electricity had a mean of 673 and a standard deviation of 556 kilowatt-hours. a. Suppose the distribution of energy use was normal. Using a ...SAT math scores follow a normal distribution with an approximate μ = 500 and σ = 100. Also ACT math scores follow a normal distribution with an approximate μ = 21 and σ = 4.7. You are an admissions officer at a ...In the National Basketball Association, the top free throw shooters usually have probability of about 0.90 of making any given free throw. a. During a game, one such player (Dolph Schayes) shot 10 free throws. Let X = number ...For the following random variables, explain why at least one condition needed to use the binomial distribution is unlikely to be satisfied. a. X = number of people in a family of size 4 who go to church on a given Sunday, ...Post your question