// Numbas version: exam_results_page_options
{"name": "Simon's copy of Probability independent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "parts": [{"customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "precision": "2", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false, "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "scripts": {}, "prompt": "<p>What is the probabilty that both of these events occur?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "{x}*{y}", "minValue": "{x}*{y}", "unitTests": [], "strictPrecision": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2"}, {"customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "precision": "2", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false, "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "scripts": {}, "prompt": "<p>What is the probabilty that neither of these events occur?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "(1-{x})*(1-{y})", "minValue": "(1-{x})*(1-{y})", "unitTests": [], "strictPrecision": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2"}, {"customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "precision": "2", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false, "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": "0", "scripts": {}, "prompt": "<p>What is the probabilty that at least one of these two events will occur?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "1-(1-{x})*(1-{y})", "minValue": "1-(1-{x})*(1-{y})", "unitTests": [], "strictPrecision": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2"}, {"customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "precision": "2", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false, "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "scripts": {}, "prompt": "<p>What is the probabilty that only one of the two events occur?</p>", "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "variableReplacements": [], "maxValue": "(1-{x})*{y}+(1-{y})*{x}", "minValue": "(1-{x})*{y}+(1-{y})*{x}", "unitTests": [], "strictPrecision": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": "2"}], "functions": {}, "name": "Simon's copy of Probability independent", "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "variable_groups": [], "ungrouped_variables": ["y", "thing", "x", "a1d", "a2", "a3", "a4", "a1", "a2d", "a3d", "a4d"], "variables": {"a3d": {"name": "a3d", "definition": "precround(1-a2,2)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "y": {"name": "y", "definition": "random(0.01..0.99#0.01)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}, "a3": {"name": "a3", "definition": "1-a2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a1": {"name": "a1", "definition": "x*y", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a2d": {"name": "a2d", "definition": "precround((1-x)*(1-y),2)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a4d": {"name": "a4d", "definition": "precround((1-x)*y+(1-y)*x,2)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a4": {"name": "a4", "definition": "(1-x)*y+(1-y)*x", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a1d": {"name": "a1d", "definition": "precround(x*y,2)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "x": {"name": "x", "definition": "random(0.01..0.9#0.01)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}, "a2": {"name": "a2", "definition": "(1-x)*(1-y)", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "thing": {"name": "thing", "definition": "random(['there will be a change in government in Ireland next year ', 'Ireland will win the rugby world cup next year'],['it will rain in Qumar on any given day','it will rain in Timbucktoo on any given day'],['shares in the Bank of Lapland will rise on any given day','shares in the Bank of Never Never Land will rise on any given day'])", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "statement": "<p>The probability that {thing[0]} is {x}, while the probability that {thing[1]} is {y}. Assume that these two events are independent. Give all answers correct to<span style=\"text-decoration: underline;\"> <strong>two decimal places</strong>.</span></p>", "advice": "<p>Let</p>\n<p>A =&nbsp;{thing[0]}</p>\n<p>and</p>\n<p>B =&nbsp;{thing[1]}</p>\n<p></p>\n<p><strong>(a)</strong></p>\n<p>Since the events are independent, we can calculate</p>\n<p>P(A and B) = P(A) $\\times$ P(B) =&nbsp;$\\var{x} \\times \\var{y}=\\var{a1}$</p>\n<p>Next round to 2 decimal places to get {precround(a1d,2)}</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>P(neither A nor B)=P(not A AND not B)= P(not A)&nbsp;$\\times$ P(not B)$=(1-\\var{x})\\times (1-\\var{y})=\\var{a2}$</p>\n<p>Next round to 2 decimal places to get {a2d}</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>P(at least one of A or B occurs) = 1 -&nbsp; P(neither A nor B) = 1 - {a2d} = {a3d}&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;using the answer from part (b)</p>\n<p><strong></strong></p>\n<p><strong>(d)</strong></p>\n<p>P(only one of A or B occurs) = P(A occurs and B doesn't OR B occurs and A doesn't)</p>\n<p>= P(A and not B) + P(B and not A)</p>\n<p>= $ \\var{x} \\times (1-\\var{y}) +&nbsp;\\var{y} \\times (1-\\var{x})=\\var{a4}$</p>\n<p>Next round to 2 decimal places to get {a4d}</p>\n<p></p>", "rulesets": {}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}