# Problem 286: Scoring probabilities

![graphic](img286.gif)

Barbara is a mathematician and a basketball player. She has found that
the probability of scoring a point when shooting from a distance x is
exactly (1 - x/q), where q is a real constant greater than 50. During
each practice run, she takes shots from distances x = 1, x = 2, ...,
x = 50 and, according to her records, she has precisely a 2 % chance to
score a total of exactly 20 points. Find q and give your answer rounded
to 10 decimal places.