Daily Tech Puzzle #15
Sponsored by MindSumo

I've got a coin here that comes up heads with probability p > 0 and tails with probability 1 - p > 0 independently on each flip.

I flip the coin 8 times.

We know that the probability of 3 heads and 5 tails is 1/25 of the probability of 5 heads and 3 tails. if p = m / n, and and and relatively prime positive integers, what is m + n?