--description--

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 ($1 - \frac{x}{q}$), where $q$ is a real constant greater than 50.

During each practice run, she takes shots from distances $x = 1, x = 2, \ldots, x = 50$ 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.

--hints--

scoringProbabilities() should return 52.6494571953.

assert.strictEqual(scoringProbabilities(), 52.6494571953);

--seed--

--seed-contents--

function scoringProbabilities() {

  return true;
}

scoringProbabilities();

--solutions--

// solution required