// 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": "
Two fair six-sided dice are rolled.
", "variable_groups": [], "extensions": ["stats"], "tags": [], "parts": [{"gaps": [{"notallowed": {"message": "Your answer has to be a fraction and not a decimal.
", "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": "Input as a fraction.
", "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": "What is the probability of at least one die showing a $\\var{number}$?
\nProbability = [[0]]
\nEnter your answer as a fraction and not a decimal.
", "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": "Rolling a pair of dice. Find probability that at least one die shows a given number.
"}, "advice": "\n \n \nLet $A$ be the event that first dice shows a $\\var{number}$ $\\Rightarrow P(A)=\\frac{1}{6}$.
\n \n \n \nLet $B$ be the event that second dice shows a $\\var{number}$ $\\Rightarrow P(B)=\\frac{1}{6}$.
\n \n \n \n$A$ and $B$ are independent events so $P(A\\cap B) = P(A)\\times P(B)$.
\n \n \n \nWe want the probability $P(A \\cup B)$ of either $A$ or $B$ showing $\\var{number}$ and
\n \n \n \n\\[\\begin{eqnarray*}\n \n P(A \\cup B) &=& P(A)+P(B)-P(A \\cap B)\\\\\n \n &=& P(A)+P(B)-P(A)P(B)\\\\\n \n &=&\\frac{1}{6}+ \\frac{1}{6}-\\frac{1}{36}\\\\\n \n &=& \\frac{11}{36}\n \n \\end{eqnarray*}\n \n \\]
\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/"}]}