Given four integers a, b, c and d. Player A & B try to score a penalty. Probability of A shooting the target is a / b while probability of B shooting the target is c / d. The player who scores the penalty first wins. The task is to find the probability of A winning the match.
Input: a = 1, b = 3, c = 1, d = 3
Input: a = 1, b = 2, c = 10, d = 11
Approach: If we consider variables K = a / b as the probability of A shooting the target and R = (1 – (a / b)) * (1 – (c / d)) as the probability that A as well as B both missing the target.
Therefore, the solution forms a Geometric progression K * R0 + K * R1 + K * R2 + ….. whose sum is (K / 1 – R). After putting the values of K and R we get the formula as K * (1 / (1 – (1 – r) * (1 – k))).
Below is the implementation of the above approach:
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