Question

Andrew has ten different two-player board games on his shelf. He has them numbered 1 through 10. When he plays the game i against Diego, he has a i^2/100 chance of winning. If Andrew rolls a fair ten-sided die to determine which game to play, the probability that he will win against Diego can be expressed as a/b where a and b are positive, coprime integers. What is the value of a+b?

Answer 1

Use a probability tree to find that the overall probability of winning is
[∑(i²)/100]/10] for i=1 to 10
=385/1000
which should be simplified to an irreduceable fraction a/b.
The sum of a+b is then 277.

Answer 2

Only question left is how Andrew found a fair 10 sided die. Platonic solids have 4,6,8,12 and 20 sides!