A board game uses two dice with unusual numbers of faces: the first die shows 1 to a and the second 1 to b, each face equally likely. A player moves only if the total of the two dice is at least target.
Write chance_to_move(a, b, target) that returns the exact probability as a tuple (numerator, denominator) in lowest terms. A probability of 0 is (0, 1) and a probability of 1 is (1, 1).
Examples
Input: a = 6, b = 6, target = 10
Output: (1, 6)
Explanation: 6 of the 36 equally likely pairs have a total of 10 or more:
(4,6) (5,5) (6,4) (5,6) (6,5) (6,6). 6/36 = 1/6.
Input: a = 4, b = 8, target = 11
Output: (3, 32)
Explanation: only (3,8), (4,7) and (4,8) out of 4 × 8 = 32 pairs.
Constraints
1 <= a, b <= 10000 <= target <= 2001
Goals
- List the equally likely outcomes of rolling two different dice
- Count the outcomes in an event and divide by the total
- Give an exact probability as a fraction in lowest terms