// Numbas version: exam_results_page_options
{"name": "Blathnaid's copy of Probability independent 2 events", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["rebelmaths"], "extensions": [], "parts": [{"prompt": "<p>What is the probabilty that both of these events occur?</p>", "strictPrecision": false, "marks": "2", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "minValue": "{x}*{y}", "showPrecisionHint": false, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "{x}*{y}", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0}, {"prompt": "<p>What is the probabilty that neither of these events occur?</p>", "strictPrecision": false, "marks": "2", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "minValue": "(1-{x})*(1-{y})", "showPrecisionHint": false, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "(1-{x})*(1-{y})", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0}, {"prompt": "<p>What is the probabilty that at least one of these two events will occur?</p>", "strictPrecision": false, "marks": "2", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "minValue": "1-(1-{x})*(1-{y})", "showPrecisionHint": false, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "1-(1-{x})*(1-{y})", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": "0"}, {"prompt": "<p>What is the probabilty that only one of the two events occur?</p>", "strictPrecision": false, "marks": "2", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "minValue": "(1-{x})*{y}+(1-{y})*{x}", "showPrecisionHint": false, "correctAnswerFraction": false, "allowFractions": false, "maxValue": "(1-{x})*{y}+(1-{y})*{x}", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0}], "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>", "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "rulesets": {}, "variables": {"a3d": {"definition": "precround(1-a2,2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a3d"}, "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": "", "group": "Ungrouped variables", "templateType": "anything", "name": "thing"}, "a3": {"definition": "1-a2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a3"}, "a4d": {"definition": "precround((1-x)*y+(1-y)*x,2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a4d"}, "y": {"definition": "random(0.01..0.99#0.01)", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "name": "y"}, "a2": {"definition": "(1-x)*(1-y)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a2"}, "a1": {"definition": "x*y", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a1"}, "x": {"definition": "random(0.01..0.9#0.01)", "description": "", "group": "Ungrouped variables", "templateType": "randrange", "name": "x"}, "a2d": {"definition": "precround((1-x)*(1-y),2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a2d"}, "a4": {"definition": "(1-x)*y+(1-y)*x", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a4"}, "a1d": {"definition": "precround(x*y,2)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a1d"}}, "advice": "<p>(a) P({thing[0]})xP({thing[1]})={x}x{y}={a1}</p>\n<p>Next round to 2 decimal places to get {a1d}</p>\n<p>(b) P(not - {thing[0]})xP(not - {thing[1]})$=(1-\\var{x})\\times (1-\\var{y})=\\var{a2}$</p>\n<p>Next round to 2 decimal places to get {a2d}</p>\n<p>(c) 1- (answer to part (b))=1-{a2d}={a3d}</p>\n<p>(d) (&nbsp;(1-{x})x {y})+(&nbsp;(1-{y})x {x})={a4}</p>\n<p>Next round to 2 decimal places to get {a4d}</p>\n<p></p>", "type": "question", "preamble": {"js": "", "css": ""}, "showQuestionGroupNames": false, "functions": {}, "ungrouped_variables": ["y", "thing", "x", "a1d", "a2", "a3", "a4", "a1", "a2d", "a3d", "a4d"], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Blathnaid's copy of Probability independent 2 events", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}