Problem:
A player chooses one of the numbers through . After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered through . If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins . If the number chosen appears on the bottom of both of the dice, then the player wins . If the number chosen does not appear on the bottom of either of the dice, the player loses . What is the expected return to the player, in dollars, for one roll of the dice?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The probability of the number appearing , and times is
respectively. So the expected return, in dollars, to the player is
The problems on this page are the property of the MAA's American Mathematics Competitions