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Find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater than 6, given that neither die is a five.

Solution

Find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater than 6, given that neither die is a five.

Solution

\frac{7}{12}

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 6 given that die is a 5:

21

Probability

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

= \frac{21}{6 ^{2}}

\frac{21}{6 ^{2}} = \frac{7}{12}

= \frac{7}{12}

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