Math CentralQuandaries & Queries


Question from Julia, a student:

What is the probability of rolling(as many times as necessary) a die and getting a total number(sum) when all the rolls are added together of 11?

Thank you.

I will assume that you are asking a question about rolling a pair of fair six-sided dice. To answer your question, first determine how many different rolls are possible. Consider a roll to consist of an ordered pair of numbers, e.g. (3,2) where the first ordinate is the result on the first die and the second ordinate is the result on the second die (thus (3,2) is different from (2,3)). Using the classical approach to probability we can assume that each of these possible rolls is equally likely. The number of possible rolls will be the denominator in your answer. Next determine how many of these rolls give a sum of 11. This is the numerator in your answer.

Dr. L. Dame

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