Question 7
A standard fair six-sided die is rolled repeatedly. Each time the die reads $1$ or $2,$ Alice gets a coin; each time it reads $3$ or $4,$ Bob gets a coin; and each time it reads $5$ or $6,$ Carol gets a coin. The probability that Alice and Bob each receive at least two coins before Carol receives any coins can be written as $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $100m + n.$