Probability Card Games: Name the Pool First

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<body class="classroom"><main><header><div class="eyebrow">Classroom practice · fictional data</div><h1>Probability Card Games: Name the Pool First</h1><p>After R1 is drawn, a learner removes every red card. That leaves the wrong pool and denominator. <mark>Remove the identified card, not its whole color</mark>, before counting the next eligible outcomes.</p></header>
<nav><button type="button" id="overall">Overall</button><button type="button" id="red">First red</button><button type="button" id="blue">First blue</button><button type="button" id="r1">First R1</button><button type="button" id="replace">With replacement</button><button type="button" id="without">Without replacement</button><button type="button" id="reset">Reset</button></nav><p id="result" class="result" role="status"></p><div id="ledger" class="ledger"></div><label for="fraction">Probability second card is red (fraction)</label><input id="fraction" type="text" value=""><nav><button type="button" id="check">Check fraction</button></nav><p id="feedback" role="status"></p>
<footer>Changing the condition or replacement rule clears the answer. Count only the displayed eligible pairs.</footer></main><script>
(()=>{'use strict';const q=id=>document.querySelector('#'+id);const set=(id,value)=>{q(id).textContent=String(value);};const on=(id,callback)=>q(id).addEventListener('click',callback);const escapeHtml=value=>String(value).replace(/[&<>"']/g,c=>({'&':'&amp;','<':'&lt;','>':'&gt;','"':'&quot;',"'":'&#39;'}[c]));const table=(id,heads,rows)=>{q(id).innerHTML='<table><thead><tr>'+heads.map(h=>'<th scope="col">'+escapeHtml(h)+'</th>').join('')+'</tr></thead><tbody>'+rows.map(row=>'<tr>'+row.map(value=>'<td>'+escapeHtml(value)+'</td>').join('')+'</tr>').join('')+'</tbody></table>';};const field=(id,label,value='')=>'<label for="'+id+'">'+escapeHtml(label)+'</label><input id="'+id+'" value="'+escapeHtml(value)+'">';const btn=(id,label)=>'<button type="button" id="'+id+'">'+escapeHtml(label)+'</button>';const fmt=value=>Number(value).toFixed(6);
(function(){const cards=['R1','R2','B1','B2'];let condition='overall',replace=false,pairs=[];function render(){pairs=cards.flatMap(a=>cards.filter(b=>replace||b!==a).map(b=>[a,b])).filter(([a])=>condition==='overall'||condition==='red'&&a[0]==='R'||condition==='blue'&&a[0]==='B'||condition==='r1'&&a==='R1');const n=pairs.filter(([,b])=>b[0]==='R').length;set('result',`${replace?'With':'Without'} replacement; ${condition}. ${pairs.length} eligible ordered pairs; ${n} end in red. Probability ${n}/${pairs.length}.`);table('ledger',['First ID','Second ID'],pairs);q('fraction').value='';set('feedback','Unanswered.');}for(const id of['overall','red','blue','r1'])on(id,()=>{condition=id;render();});on('replace',()=>{replace=true;render();});on('without',()=>{replace=false;render();});on('check',()=>{const raw=q('fraction').value.trim();if(!/^\d+\s*\/\s*\d+$/.test(raw))return set('feedback','Enter a fraction such as 1/3; blank is unanswered.');const[a,b]=raw.split('/').map(part=>BigInt(part.trim())),n=pairs.filter(([,x])=>x[0]==='R').length;if(b===0n)return set('feedback','Denominator must be positive.');set('feedback',a*BigInt(pairs.length)===b*BigInt(n)?'Equivalent fraction: correct for this eligible pool.':'Recount favorable pairs and this question’s denominator.');});q('fraction').addEventListener('input',()=>set('feedback','Answer changed; check again.'));on('reset',()=>{condition='overall';replace=false;render();});render();})();})();
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