Art of Problem Solving

2022 AMC 12B Problems/Problem 12: Difference between revisions

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== Problem ==


Kayla rolls four fair <math>6</math>-sided dice. What is the probability that at least one of the numbers Kayla rolls is greater than <math>4</math> and at least two of the numbers she rolls are greater than <math>2</math>?
<math>\textbf{(A)}\ \frac{2}{3} \qquad
\textbf{(B)}\ \frac{19}{27} \qquad
\textbf{(C)}\ \frac{59}{81} \qquad
\textbf{(D)}\ \frac{61}{81} \qquad
\textbf{(E)}\ \frac{7}{9}</math>
== Solution ==
== See Also ==
{{AMC12 box|year=2022|ab=B|num-b=11|num-a=13}}
{{MAA Notice}}

Revision as of 20:29, 17 November 2022

Problem

Kayla rolls four fair $6$-sided dice. What is the probability that at least one of the numbers Kayla rolls is greater than $4$ and at least two of the numbers she rolls are greater than $2$?

$\textbf{(A)}\ \frac{2}{3} \qquad  \textbf{(B)}\ \frac{19}{27} \qquad  \textbf{(C)}\ \frac{59}{81} \qquad  \textbf{(D)}\ \frac{61}{81} \qquad  \textbf{(E)}\ \frac{7}{9}$

Solution

See Also

2022 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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 12 Problems and Solutions

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