Question

There is an octahedral (8-faces) die whose faces each have one different number from the set {1, 2, 3, 4, 5, 6, 7, 8}. The die is rolled twice, and the number appearing on top after the first roll is multiplied by the number appearing on top after the second roll. What is the probability that this product is divisible by 9?

Answer 1

the only rolls that are divisible by 9 are 33, 36, 63 and 66
So, 4/64 is what you get

Answer 2

It can only be divisible by 9 if the number on each roll is divisible by 3, i.e. is 3 or 6. There is a2/8 chance of this on each roll so the probability is 2/8 x 2/8 = 1/16.

Answer 3

nothing

Answer 4

Getting a number from rolling an octahedral (8-sided) die.