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What is the probability that the sum of the numbers coming up when rolling three dice is greater than 16?

Solution

What is the probability that the sum of the numbers coming up when rolling three dice is greater than 16?

Solution

\frac{1}{54}

Solution steps

The possible outcomes when three dice are rolled are

6 \cdot 6 \cdot 6

Therefore, the number of possible outcomes:

6^{3}

Find the number of favorable outcomes of the sum of the numbers coming up when rolling 3 dice is greater than 16:

4

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{4}{6 ^{3}}

\frac{4}{6 ^{3}} = \frac{1}{54}

= \frac{1}{54}

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