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What is the probability of rolling a number less than or equal to 8 with the

sum of two dice, given that at least one of the dice must show a 6?

1 Answer

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Explanation:

this is a combined event.

a probability is always the ratio

desired outcomes / totally possible outcomes

in our experiment with rolling 2 dice we have totally 6×6 = 36 different outcomes.

from these 36 total possibilities we desire the following (sum is less than or equal to 8, one die has to show a 6) :

6 1

6 2

1 6

2 6

that is 4 desired outcomes.

and the probabilty for this is

4/36 = 1/9 = 0.111111111...

in mathematical terms we could say :

one possible scenario is one die is 6, and the other is either 1 or 2.

the probability for one die to show 6 is

1/6

the probability for one die to show 1 or 2 is

2/6.

the probabilty for the combination is then

1/6 × 2/6 = 2/36 = 1/18

how many different combinations can we have ?

well, with 2 dice we have 2 such possible combinations.

therefore, the probability is

2 × 1/18 = 2/18 = 1/9.

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