Difference between revisions of "2020 AMC 10A Problems/Problem 25"

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Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly <math>7.</math> Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?
 
Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly <math>7.</math> Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?
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==See Also==
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{{AMC10 box|year=2019|ab=B|num-b=24|after=Last Problem}}
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{{MAA Notice}}

Revision as of 21:06, 31 January 2020

Jason rolls three fair standard six-sided dice. Then he looks at the rolls and chooses a subset of the dice (possibly empty, possibly all three dice) to reroll. After rerolling, he wins if and only if the sum of the numbers face up on the three dice is exactly $7.$ Jason always plays to optimize his chances of winning. What is the probability that he chooses to reroll exactly two of the dice?

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Last Problem
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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