A tetrahedral, or four-sided die, can come up 1, 2, 3, or 4. The outcome of a single roll is the number at the base of the pyramid (see the figure on the right).
Tetrahedral Chuck-a-Buck is a game played with a pair of tetrahedral dice. A player bets $1 on one of the numbers—1, 2, 3, or 4— and the dice are rolled. If the player's number appears on exactly one of the dice, she receives $1.50 plus her own $1 back; if the player's number appears on both dice, she receives $2 plus her original $1 stake.
a) How many outcomes are there when two tetrahedral dice are rolled? (Assume one of the dice is red and the other green. An outcome is a pair of numbers denoting what is on each of the dice; for example, (3, 2) if 3 is on red and 2 on green.)
b) What is the probability that exactly one of the dice matches the player's number?
c) What is the probability that both of the dice match the player's number?
d) What is the player's expected loss per game