Rosencrantz chooses a coin from Guildenstern collection of one hundred pennies and promptly tosses six heads in a row. While rhapsodizing over his good luck, he learns that four of the pennies were two-headed. The probability that Rosencrantz chose one of the two-headed pennies given that he flipped six heads in a row can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m n$.