2a:null 2b:["$","title",null,{"children":"Sample spaces | Pierre PC | Observable"}] 30:[] 2e:{"id":"81aebdc709f5374b","slug":"sample-spaces","title":"Sample spaces","thumbnail":"99b08fdc47faee1f937ada8e645be679dc282f6996b8c8a3fd2106a2eae1cc27","access_level":"public","create_time":"$D2020-01-21T20:19:16.621Z","update_time":"$D2020-01-22T06:37:29.539Z","view_time":null,"first_public_time":"$D2020-01-22T04:50:28.619Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"e63037398666117f","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":"starter_2024"},"version":341,"publish_version":341,"role":null,"authored":false,"authors":[{"type":"individual","id":"e1fb4a1ab7bf50c7","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":null}],"members":[{"type":"individual","id":"e1fb4a1ab7bf50c7","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":1,"collection":{"id":"ac21ca0b7e8ed20d","slug":"probability-course","title":"Probability course","owner":{"id":"e63037398666117f","login":"pierrepc","name":"Pierre PC"}},"type":"notebook","body":{"title":"Sample spaces","cells":[{"id":0,"value":"md`# Sample spaces\n\nHere are three examples of possible sample spaces for the sum of two dice. The event *The sum is precisely ${S}* is highlighted. You can modify this number below.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":118,"value":"viewof S = {\n const element = html`

Target sum:

`;\n element.addEventListener(\"change\", () => element.dispatchEvent(new CustomEvent(\"input\")));\n element.addEventListener(\"input\", () => element.value = inputValue(element));\n element.value = inputValue(element);\n return element;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2,"value":"{ const intro = `1. The simplest sample space possible: the collection of possible values for the sum.

`\n let s = lineArray(x, (j) => j === S, j => `${j}`);\n s = s.map((l) => l.join(\", \"))\n .join(`,
`);\n return html`${intro}S₁ = \\{ ${s} \\}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":58,"value":"{ const intro = `2. A very natural space: that of all possible ordered pairs. Note that every outcome has the same probability.

`\n let s = lineArray(y, (j) => j[0]+j[1] === S, j => `(${j[0]},${j[1]})`);\n s = s.map((l) => l.join(`, `))\n .join(`,
S₂ = \\{ `);\n return html`${intro}S₂ = \\{ ${s} \\}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":94,"value":"{ const intro = `3. Another space that comes to mind: the set where the pairs are unordered. Each element of the leftmost column is twice as likely as any other.

`\n let s = lineArray(z, (j) => j[0]+j[1] === S, j => `\\{${j[0]},${j[1]}\\}`);\n s = s.map((l) => l.join(`, `))\n .join(`,
S₃ = \\{ `);\n return html`${intro}S₃ = \\{ ${s} \\}`; }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":252,"value":"{ const fractions = [`1/36`,`1/18`,`1/12`,`1/9`,`5/36`,`1/6`]\n let i = Math.min(S-2,12-S)\n return md`ℙ( The sum of the two dice is ${S} ) = ${fractions[i]}`;\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":103,"value":"md`### *Don't bother reading below this point*\n(Unless you like to read code...)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":20,"value":"x = [Array.from({length: 11}, (a,i) => i+2)];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":47,"value":"y = Array.from({length: 6}, function (a,i){\n return Array.from({length: 6}, function (b,j){\n return [i+1,j+1];\n });\n });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":83,"value":"z = Array.from({length: 6}, function (a,i){\n return Array.from({length: 6-i}, function (b,j){\n return [i+1,j+i+1];\n });\n });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":165,"value":"lineArray = function (x, belongs, name) {\n let line = [];\n let lines = [];\n x.forEach(function (i) {\n line = [];\n i.forEach(function (j) {\n if (belongs(j)) {\n line.push(`${name(j)}`);\n }\n else {\n line.push(`${name(j)}`);\n }\n });\n lines.push(line)\n });\n return lines;\n };","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":320,"value":"inputValue = function (element) {\n let input = element.getElementsByTagName(`input`)[0];\n return parseInt(input.value);\n } ;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":68,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2f:"$2e:body"