// Numbas version: exam_results_page_options
{"name": "Roll a pair of dice - find probability at least one die shows a given number, , , ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>Two fair six-sided dice are rolled.</p>", "variable_groups": [], "extensions": ["stats"], "tags": [], "parts": [{"gaps": [{"notallowed": {"message": "<p>Your answer has to be a fraction and not a decimal.</p>", "strings": ["."], "showStrings": false, "partialCredit": 0}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "marks": "2", "type": "jme", "answer": "11/36", "variableReplacements": [], "checkingaccuracy": 0.001, "showFeedbackIcon": true, "musthave": {"message": "<p>Input as a fraction.</p>", "strings": ["/", 11, 36], "showStrings": false, "partialCredit": 0}, "scripts": {}, "showpreview": true, "showCorrectAnswer": true, "checkingtype": "absdiff", "answersimplification": "std, fractionNumbers", "expectedvariablenames": [], "vsetrangepoints": 5}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>What is the probability of at least one die showing a $\\var{number}$?</p>\n<p>Probability = [[0]]</p>\n<p>Enter your answer as a fraction and not a decimal.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "variables": {"number": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..6)", "name": "number", "description": ""}}, "name": "Roll a pair of dice - find probability at least one die shows a given number, , , ", "preamble": {"css": "", "js": ""}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Rolling a pair of dice. Find probability that at least one die shows a given number.</p>"}, "advice": "\n    \n    \n    <p>Let $A$ be the event that first dice shows a $\\var{number}$  $\\Rightarrow P(A)=\\frac{1}{6}$.</p>\n    \n    \n    \n    <p>Let $B$ be the event that second dice shows a $\\var{number}$ $\\Rightarrow P(B)=\\frac{1}{6}$.</p>\n    \n    \n    \n    <p>$A$ and $B$ are independent events so $P(A\\cap B) = P(A)\\times P(B)$.</p>\n    \n    \n    \n    <p>We want the probability $P(A \\cup B)$ of either $A$ or $B$ showing $\\var{number}$ and</p>\n    \n    \n    \n    <p>\\[\\begin{eqnarray*}\n    \n    P(A \\cup B) &#38;=&#38; P(A)+P(B)-P(A \\cap B)\\\\\n    \n    &#38;=&#38; P(A)+P(B)-P(A)P(B)\\\\\n    \n    &#38;=&#38;\\frac{1}{6}+ \\frac{1}{6}-\\frac{1}{36}\\\\\n    \n    &#38;=&#38; \\frac{11}{36}\n    \n    \\end{eqnarray*}\n    \n    \\]</p>\n    \n    \n    ", "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["number"], "type": "question", "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}]}], "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}