2007 AMC 10B Problems/Problem 22
Contents
Problem 22
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 has been rolled, then the player wins dollar. If the number chosen appears on the bottom of both of the dice, then the player wins dollars. If the number chosen does not appear on the bottom of either of the dice, the player loses dollar. What is the expected return to the player, in dollars, for one roll of the dice?
Solution
There are ways for your number to show up once, way for your number to show up twice, and ways for your number to not show up at all. Think of this as a set of sixteen numbers with six 's, one , and nine 's. The average of this set is the expected return to the player.
Solution 2
We approach this through casework. We have a chance of earning dollar. We have a chance of earning dollars, and a chance of losing dollar. Thus, our final answer is -SuperJJ
See Also
2007 AMC 10B (Problems • Answer Key • Resources) | ||
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Followed by Problem 23 | |
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