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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 9, given that neither die is a six

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 9, g i v e n t ha t n e i t h er d i e i s a s i x

Solution

\frac{1}{6}

+1

Decimal

0.16666 \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 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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