// Numbas version: exam_results_page_options
{"name": "Probability: Conditional probability 4 - two-way table", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Probability: Conditional probability 4 - two-way table", "tags": [], "metadata": {"description": "<p>Calculate P(A|B) given a two-way table.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>$\\var{total}$ items are sampled with the following results:</p>\n<table border=\"1\" cellspacing=\"10\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td></td>\n<td>&nbsp; &nbsp;$\\var{nB}$ &nbsp;&nbsp;</td>\n<td>&nbsp;not $\\var{nB}$&nbsp;</td>\n<td>&nbsp; TOTAL &nbsp;</td>\n</tr>\n<tr>\n<td>&nbsp; &nbsp;$\\var{nA}$ &nbsp;&nbsp;</td>\n<td>&nbsp;$\\var{AnB}$</td>\n<td>&nbsp;$\\var{AnB'}$&nbsp;</td>\n<td>&nbsp;$\\var{A}$&nbsp;</td>\n</tr>\n<tr>\n<td>&nbsp;not $\\var{nA}$&nbsp;</td>\n<td>&nbsp;$\\var{notAnB}$&nbsp;</td>\n<td>&nbsp;$\\var{notAnB'}$</td>\n<td>&nbsp;&nbsp;$\\var{total-A}$</td>\n</tr>\n<tr>\n<td>&nbsp;TOTAL&nbsp;</td>\n<td>&nbsp;$\\var{B}$</td>\n<td>&nbsp;&nbsp;&nbsp;$\\var{total-B}$</td>\n<td>$\\var{total}$</td>\n</tr>\n</tbody>\n</table>", "advice": "<p></p>\n<p>We can use the formula:</p>\n<p>$P(A \\vert B) = \\frac{P(A \\cap B)}{P(B)}$</p>\n<p>$P(\\var{q2b} \\vert \\var{q2a}) = \\frac{P(\\var{q2b} \\cap \\var{q2a})}{P(\\var{q2a})}$</p>\n<p>$P(\\var{q2b} \\vert \\var{q2a}) = \\var[fractionnumbers]{q2}$.<br/><br/></p>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"nA": {"name": "nA", "group": "Final data", "definition": "pairs[0]", "description": "", "templateType": "anything", "can_override": false}, "pairs": {"name": "pairs", "group": "Final data", "definition": "random(['Section A','Category M'],['Phenotype A','Phenotype 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notAnB\n", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Final data", "definition": "AnB+AnB'", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Final data", "definition": "notAnB + AnB", "description": "", "templateType": "anything", "can_override": false}, "q1a": {"name": "q1a", "group": "Final data", "definition": "if(isornot1=0,\"not {pairs[0]}\",pairs[0])", "description": "", "templateType": "anything", "can_override": false}, "q2a": {"name": "q2a", "group": "Final data", "definition": "if(isornot3=0,\"not {pairs[0]}\",pairs[0])", "description": "", "templateType": "anything", "can_override": false}, "q1b": {"name": "q1b", "group": "Final data", "definition": "if(isornot2=0,\"not {pairs[1]}\",pairs[1])", "description": "", "templateType": "anything", "can_override": false}, "q2b": {"name": "q2b", "group": "Final data", "definition": "if(isornot4=0,\"not {pairs[1]}\",pairs[1])", 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