数学 - JavaScript - 確からしさをみる - 確率 – 条件つき確率と確率の乗法定理 - いくつかの例

数学読本〈4〉

学習環境

• Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
• Windows 10 Pro (OS)
• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

数学読本〈4〉数列の極限，順列/順列・組合せ/確率/関数の極限と微分法(松坂 和夫(著)、岩波書店)の第16章(確からしさをみる - 確率)、16.2(条件つき確率と確率の乗法定理)、いくつかの例、問19、20、21、22.を取り組んでみる。

19. 
    $\frac{1}{6^3}=\frac{1}{216}$
20. 
    $\begin{array}{l}P\left(A\right)=1-{\left(\frac{1}{2}\right)}^2=\frac{3}{4}\\ P\left(A\cap B\right)=\frac{1}{4}\\ P_A\left(B\right)=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}\end{array}$
21. 1. 
       $P\left(A\right)=\frac{3}{6}·\frac{3}{6}+\frac{3}{6}·\frac{3}{6}=\frac{1}{2}$
    2. 
       $P\left(B\right)=1-{\left(\frac{5}{6}\right)}^2=\frac{11}{36}$
    3. 
       $\begin{array}{l}P\left(A\cap B\right)=\frac{1}{6}·\frac{3}{6}+\frac{3}{6}·\frac{1}{6}-\frac{1}{6}·\frac{1}{6}=\frac{5}{36}\\ P_A\left(B\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)}=\frac{5·2}{36}=\frac{5}{18}\end{array}$
    4. 
       $P_B\left(A\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{5}{11}$
22. 
    $\frac{13}{52}·\frac{13}{51}·2=\frac{1}{2}·\frac{13}{51}=\frac{13}{102}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
回数: <input id="n0" type="number" min="1" step="1" value="5000">
<br>
<button id="run0">run</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>
<script src="sample19.js"></script>    

JavaScript

let pre0 = document.querySelector('#output0'),
    input_n = document.querySelector('#n0'),
    btn0 = document.querySelector('#run0'),
    btn1 = document.querySelector('#clear0'),
    div0 = document.querySelector('#graph0'),
    width = 600,
    height = 600,
    padding = 50,
    p = (x) => pre0.textContent += x + '\n';

let range = (n) => {
    let result = [];
    for (let i = 0; i < n; i += 1) {
        result.push(i);
    }
    return result;
};

let f = (n) =>
    range(n)
    .map(() => {
        let a = Math.floor(Math.random() * 6) + 1,
            b = Math.floor(Math.random() * 6) + 1,
            c = Math.floor(Math.random() * 6) + 1;

        return a === 1 && b === 2 && c === 3;
    })
    .filter((bln) => bln)
    .length / n;

let output = () => {
    let n = parseInt(input_n.value, 10),
        points = [],
        result,
        t;
    
    p('19.');
    for (let i = 1; i <= n; i += 1) {
        points.push([i, f(i)]);
    }
    t = points[points.length - 1][1];
    result = 1 / 216;
    p(t ===  result);
    p(t);
    p(result);
    p(Math.abs(t - result));

    let xscale = d3.scaleLinear()
        .domain([1, n])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([Math.min(...ys), Math.max(...ys)])
        .range([height - padding, padding]);

    let xaxis = d3.axisBottom().scale(xscale);
    let yaxis = d3.axisLeft().scale(yscale);
    div0.innerHTML = '';
    let svg = d3.select('#graph0')
        .append('svg')
        .attr('width', width)
        .attr('height', height);

    svg.selectAll('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', 1)
        .attr('fill', 'green');

    svg.append('g')
        .attr('transform', `translate(0, ${height - padding})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${padding}, 0)`)
        .call(yaxis);
};

input_n.onchange = output;
btn0.onclick = output;
btn1.onclick = () => pre0.textContent = '';

output();

回数: