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find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater than 9, given that neither die is a six

Solution

find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater than 9, given that neither die is a six

Solution

\frac{1}{6}

Solution steps

The possible outcomes when two dice are rolled are

6 \cdot 6

Therefore, the number of possible outcomes:

6^{2}

Find the number of favorable outcomes of in a single roll of 2 fair 6 -sided dice that the sum is greater than 9 given that die is a 6:

6

Probability

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

= \frac{6}{6 ^{2}}

Cancel the common factor:

6

= \frac{1}{6}

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