Question

I have a fair 12-sided (dodecahedron) die with sides labelled 1, 2, …, 12 respectively. See https://images.app.goo.gl/FGseg31kiTAW7psK6 for an example of a fair 12-sided die. I also have a fair 6-sided die with sides labelled 1, 2, …, 6 respectively. I roll the first die on a table with a standard protocol, then roll the second die on another table also with a standard protocol. What is the probability that the sum of the numbers appearing face up on the two dice is 11?

Answer 1

Solution

The combinations of the dies whose sum will give 11 are:

(5 & 6) or (6 & 5) or (7 & 4) or (8 & 3) or (9 & 2) or (10 & 1).

Thus there are 6 possible combinations each with equal possibility of occurrence.

The probability of getting a certain value when the 12-sided die is rolled is $1 \over 12$

The probability of getting a certain value when the 6-sided die is rolled is $1 \over 6$

Thus the probability is:

$$\big( {1 \over 6} * {1 \over 12} \big) *6 = {1 \over 12}$$

Answer: $1 \over 12$