// Numbas version: exam_results_page_options
{"name": "Select a card and roll a dice", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Select a card and roll a dice", "tags": ["probability", "Probability", "rebel", "REBEL", "Rebel", "rebelmaths"], "metadata": {"description": "<p>A student selects a card from a deck of 52 and rolls a dice once.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Please give your answers to 3 decimal places.</strong></p>\n<p>A student selects one card at random from a pack of 52 playing cards and then rolls a dice once.</p>\n<p>Let event $A$ be that the card she picks is a $\\var{suit}$.</p>\n<p>Let event $B$ be that the number she rolls is greater than $\\var{n}$.</p>", "advice": "<p>The outcome of selecting the card is&nbsp;<strong>independent</strong>&nbsp;of (not effected by) the outcome of rolling the dice.</p>\n<p>If two events, $A$ and $B$, are independent then $P(A\\cap B)=P(A)\\times P(B)$.</p>\n<p><strong>Part a)</strong></p>\n<address></address>\n<p>Let $A$ represent the event that a $\\var{suit}$ is selected and let $B$ represent the event that a number greater than $\\var{n}$ is rolled.</p>\n<p>&nbsp;$P(A)$ is $\\frac{13}{52}=\\frac{1}{4}$ and $P(B)$ is &nbsp;$\\frac{\\var{6-n}}{6}$.</p>\n<p>Therefore the probability of drawing a $\\var{suit}$ and rolling a number greater than $\\var{n}$ is $ P(A) \\times P(B)=\\frac{1}{4} \\times \\frac{\\var{6-n}}{6}$.&nbsp;</p>\n<p><strong>Part b)</strong></p>\n<p></p>\n<p>The probability that neither of these events occur is the probability of not drawing a $\\var{suit}$ which is $P(A^c)=\\frac{3}{4}$ mulitiplied by the probability of not rolling a number greater than $\\var{n}$ which is&nbsp;$P(B^c)=\\frac{\\var{n}}{6}$&nbsp;.</p>\n<p><strong>Part c)</strong></p>\n<p>The probability that only one of these events occur is $P(A ^c\\cap B)+P(A \\cap B^c)=(\\frac{3}{4} \\times \\frac{\\var{6-n}}{6})+(\\frac{1}{4} \\times \\frac{\\var{n}}{6})$.</p>\n<p><strong>Part d)</strong></p>\n<p>The probability &nbsp;that at least one of these two events will occur is $1- P$(neither of the events occur)$=1-(P(A^c)\\times P(B^c))= 1-(\\frac{3}{4}\\times \\frac{\\var{n}}{6})$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "<p>number on dice is greater than n.</p>", "templateType": "anything", "can_override": false}, "suit": {"name": "suit", "group": "Ungrouped variables", "definition": "random ('diamond','spade','heart','club')", "description": "<p>suit</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "suit"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the probability that the card she picks is a $\\var{suit}$ and the number she rolls is greater than $\\var{n}$.</p>", "minValue": "(1/4)*((6-n)/6)-0.001", "maxValue": "(1/4)*((6-n)/6)+0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the 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"strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the probability that only one of these two events will occur.</p>", "minValue": "((1/4)*(n/6)+(3/4)*((6-n)/6))-0.001", "maxValue": "((1/4)*(n/6)+(3/4)*((6-n)/6))+0.001", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct 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