Roll, roll, roll

Probability Level 3

You have a 6 sided die, an 8 sided die, and a 12 sided die each numbered 1 through $n$ where $n$ is the number of sides, and you roll them in that order.

What is the probability that each roll is greater than or equal to the previous roll?

The answer is 0.43.

1 solution

Mark Hennings
Jan 8, 2019

Conditioning on the value of the $8$ -sided die, the probability is $\frac{1}{8} \sum_{j=1}^8 \frac{\mathrm{min}(j,6)}{6} \times \frac{13-j}{12} \; = \; \boxed{\frac{31}{72}}$

Ah, nice compact solution! :-)

Geoff Pilling - 2 years, 5 months ago

Roll, roll, roll

The answer is 0.43.

1 solution

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