---
id: 5900f48a1000cf542c50ff9d
title: 'Problem 286: Scoring probabilities'
challengeType: 5
forumTopicId: 301937
dashedName: problem-286-scoring-probabilities
---

# --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`.

```js
assert.strictEqual(scoringProbabilities(), 52.6494571953);
```

# --seed--

## --seed-contents--

```js
function scoringProbabilities() {

  return true;
}

scoringProbabilities();
```

# --solutions--

```js
// solution required
```