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Popular Word Problems >

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

F in d t h e co n d i t i o na l ​ p ro babi l i t y, in a s in g l e ro ll o f tw o f ai r ​ 6 - s i d e d d i ce, t ha t t h e s u m i s g re a t er t han 6​, g i v e n t ha t n e i t h er d i e i s a f i v e .

Solution

\frac{7}{12}

+1

Decimal

0.58333 \dots

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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