## Scoring probabilities

### Problem 286

Published on Saturday, 3rd April 2010, 05:00 am; Solved by 1083

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.