ExplanationBecause this problem is asking for an “at least” solution, use the 1 – x shortcut.

The probability that at least one roll results in a number greater than 4 is equal to 1 minus the probability that both of the rolls result in numbers 4 or lower. For one roll, there are 6 possible outcomes (1 through 6) and 4 ways in which the outcome can be 4 or lower, so the probability is \(\frac{4}{6}=\frac{2}{3}\).

Thus, the probability that both rolls result in numbers 4 or lower is \(\frac{2}{3}\frac{2}{3}=\frac{4}{9}\).

This is the result that you do not want; subtract this from 1 to get the probability that you do want. The probability that at least one of the rolls results in a number greater than 4 is \(1 - \frac{4}{9} =\frac{5}{9}\).

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Sandy

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