A Fibonacci die has the numbers1 1 2 3 5 and 8on it if two are thrown what is the probability that the number on one die is larger than the number on the other?

Answer 1

Prob( Number on one die is larger than that on the other)

= 1 - Prob(Number on both dice is the same).

If the two 1s are distinguished as 1 and 1', then the favourable outcomes are (1,1), (1,1'), (1',1), (1',1'), (2,2), (3,3), (5,5) and (8,8) - eight of them in all.

So 1 - Prob(Number on both dice is the same)

= 1 - 8/36 = 1 - 2/9 = 7/9