2012 UNCO Math Contest II Problems/Problem 8


An ordinary fair die is tossed repeatedly until the face with six dots appears on top. On average, what is the sum of the numbers that appear on top before the six? For example, if the numbers $3, 5, 2, 2, 6$ are the numbers that appear, then the sum of the numbers before the six appears is $3+5+2+2=12$. Do not include the $6$ in the sum.


The probability that a six is rolled on any given roll is $1/6$, so on average it will take $6$ rolls to roll a six, meaning there will be an average of five rolls before the first $6$. Since these $5$ rolls could be any of $1,2,3,4,$ or $5$, their average value is $3$, so the answer is $3 \cdot 5=15$

See Also

2012 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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