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 pyram
id (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?
