2022 AMC 10B Problems/Problem 12
Contents
Problem
A pair of fair -sided dice is rolled
times. What is the least value of
such that the probability that the sum of the numbers face up on a roll equals
at least once is greater than
?
Solution
Rolling a pair of fair -sided dice, the probability of getting a sum of
is
Regardless what the first die shows, the second die has exactly one outcome to make the sum
We consider the complement: The probability of not getting a sum of
is
Rolling the pair of dice
times, the probability of getting a sum of
at least once is
Therefore, we have or
Since,
the least integer
satisfying the inequality is
~MRENTHUSIASM
Solution 2=
See Also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AMC 10 Problems and Solutions |
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