Dice!

Probability Level 4

A pair of honest dice is thrown repeatedly. What is the probability of two sums of 7 7 appear before three sums of 3 3 ?

Your answer must be in the form of an irreducible fraction a b \frac{a}{b} . Find the difference: b − a b-a .


The answer is 13.

Dieuler Oliveira by Dieuler Oliveira , 34, Brazil

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1 solution

Bill Bell
Sep 3, 2015

One need only consider outcomes of 7 or 3, whose probabilities are 3/4 and 1/4 respectively. There are four patterns by which two 7s can occur before three 3s: 

1
2
3
4
5
6
 
3, 3, 7, 7
3, 7, 3, 7
3, 7, 7
7, 3, 3, 7
7, 3, 7
7, 7

Obtaining the answer is a matter of summing the probabilities of these six outcomes.

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