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.