Roll the dice thrice 3

Probability Level 4

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

The probability of getting a sum of 4 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 I , Part II .

Image Credit: Flickr Gard Rimestad .

The answer is 79.

1 solution

Ricardo Moritz Cavalcanti
Feb 18, 2021

There are 21 outcomes that give a sum of 4, from a total of $6^3 = 216$ possible outcomes: (1) (-2,3,3) + 2 permutations; (2) (-1,2,3) + 5 permutations; (3) (0,1,3) + 5 permutations; (4) (0,2,2) + 2 permutations, and (5) (1,1,2) + 2 permutations.

Therefore, the probability of getting a sum of 4 is $\frac{21}{216}=\frac{7}{72}$ , from which follows that $a=7$ , $b = 72$ , and $\boxed{a+b=79}\,$ .

Roll the dice thrice 3

Try these too: Part I , Part II .

Image Credit: Flickr Gard Rimestad .

The answer is 79.

1 solution

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