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counting and probability junior
Problem
Allison, Brian and Noah each have a 6-sided cube. All of the faces on Allison's cube have a 5. The faces on Brian's cube are numbered 1, 2, 3, 4, 5 and 6. Three of the faces on Noah's cube have a 2 and three of the faces have a 6. All three cubes are rolled. What is the probability that Allison's roll is greater than each of Brian's and Noah's? Express your answer as a common fraction.
Solution
Since Allison will always roll a 5, we must calculate the probability that both Brian and Noah roll a 4 or lower. The probability of Brian rolling a 4 or lower is since Brian has a standard die. Noah, however, has a probability of rolling a 4 or lower, since the only way he can do so is by rolling one of his 3 sides that have a 2. So, the probability of both of these independent events occurring is .
Final answer
\frac{1}{3}