Roll the dice thrice 1

Probability Level 3

A fair dice is numbered with $1,-2,0,-1,3,2$ on its faces.

The probability of getting a sum of 6 after rolling the dice thrice can be expressed as $\frac{a}{b}$ where $a,b$ are relatively prime.

Find $a+b$ .

Try these too: Part II , Part III

Image Credit: Flickr Gard Rimestad .

The answer is 113.

1 solution

Aditya Virani Staff
Jun 11, 2015

Possible results of the three trials (unordered) are $(1,2,3),(2,2,2),(0,3,3).$ There are 6 ways to order $(1,2,3),$ 1 way to order $(2,2,2),$ and 3 ways to order $(0,3,3),$ which gives the probability $\frac{6+1+3}{6^3}=\frac{5}{108}.$

Roll the dice thrice 1

Try these too: Part II , Part III

Image Credit: Flickr Gard Rimestad .

The answer is 113.

1 solution

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