yaworsw/euler-manager

---
:id: 286
:name: Scoring probabilities
:url: https://projecteuler.net/problem=286
:content: |+
  Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance <var>x</var> is exactly (1 -&nbsp;<sup><var>x</var></sup>/<sub><var>q</var></sub>), where <var>q</var> is a real constant greater than 50.

  During each practice run, she takes shots from distances <var>x</var> = 1, <var>x</var> = 2, ..., <var>x</var> = 50 and, according to her records, she has precisely a 2 % chance to score a total of exactly 20 points.

  Find <var>q</var> and give your answer rounded to 10 decimal places.