// Numbas version: exam_results_page_options
{"name": "Convert gambling odds to probabilities, , ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"wdw": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'A bookmaker lists'", "description": "", "name": "wdw"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(0..20)", "description": "", "name": "t"}, "player1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'Australia'", "description": "", "name": "player1"}, "odds22": {"templateType": "anything", "group": "Ungrouped variables", "definition": "round(odds12*odds21/odds11)-random(2..5 except round(odds12*odds21/odds11))", "description": "", "name": "odds22"}, "den2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "odds21+odds22", "description": "", "name": "den2"}, "odds21": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(8..20)", "description": "", "name": "odds21"}, "between": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'between'", "description": "", "name": "between"}, "odds12": {"templateType": "anything", "group": "Ungrouped variables", "definition": "round((t*round(odds11+1)/2+(20-t)*(odds11-1))/20)", "description": "", "name": "odds12"}, "odds11": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(8..20)", "description": "", "name": "odds11"}, "event": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'the next series of games'", "description": "", "name": "event"}, "player2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'England'", "description": "", "name": "player2"}, "den1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "odds11+odds12", "description": "", "name": "den1"}}, "ungrouped_variables": ["odds12", "odds11", "den2", "den1", "wdw", "player2", "player1", "t", "between", "odds22", "event", "odds21"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Convert gambling odds to probabilities, , ", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "{odds11}/{den1}", "musthave": {"message": "<p>Input as a fraction.</p>", "showStrings": false, "partialCredit": 0, "strings": ["/"]}, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input your answer as a fraction and not a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std, fractionNumbers", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>You should take the bet if you think that $\\Pr(\\var{player1}\\text{ win})$ is greater than [[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{odds22}/{den2}", "musthave": {"message": "<p>Input as a fraction.</p>", "showStrings": false, "partialCredit": 0, "strings": ["/"]}, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input your answer as a fraction and not a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std, fractionNumbers", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>You should take the bet if you think that $\\Pr(\\var{player2}\\text{ win})$ is greater than [[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>The following odds are given for {event} {between} {player1} and {player2}</p>\n<table border=\"3\">\n<tbody>\n<tr>\n<td>{player1} $\\var{odds11}: \\var{odds12}$ on</td>\n<td>{player2} $\\var{odds21}: \\var{odds22}$ against</td>\n</tr>\n</tbody>\n</table>\n<p>Convert these statements about odds into probabilities.</p>\n<p>Give your answers as fractions.</p>", "tags": ["checked2015", "converting odds", "elementary probability", "MAS1604", "MAS8380", "MAS8401", "odds", "odds into probabilities", "probability", "Probability", "statistics", "tested1"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/07/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Added decimal point as forbidden string for both answers.</p>\n        <p>Checked calculation.</p>\n        <p><strong>22/07/2012:</strong></p>\n        <p>Added description.</p>\n        <p><strong>31/07/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Question appears to be working correctly.</p>\n        <p><strong>20/12/2012:</strong></p>\n        <p>Checked calculations, OK. Added tested1 tag.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Converting odds to probabilities.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<h4>a)</h4>\n<p>Odds of $\\var{odds11}: \\var{odds12}$ on means that you should take the bet if you think the probability of {player1} <em> winning </em> is greater than:</p>\n<p>\\[ \\frac{\\var{odds11}}{\\var{odds11}+\\var{odds12}} = \\simplify[std]{{odds11}/{odds11+odds12}}\\]</p>\n<h4>b)</h4>\n<p>Odds of $\\var{odds21}: \\var{odds22}$ against means that you should take the bet if you think that the probability of {player2} <em> losing </em> is less than:</p>\n<p>\\[ \\frac{\\var{odds21}}{\\var{odds21}+\\var{odds22}} = \\simplify[std]{{odds21}/{odds21+odds22}}\\]</p>\n<p>That is, if you think the probability of {player2} <em>winning</em> is greater than:</p>\n<p>\\[ 1- \\simplify[std]{{odds21}/{odds21+odds22}}=\\simplify[std]{{odds22}/{odds21+odds22}}\\]</p>\n<p>Note that the sum of these probabilities is:</p>\n<p>\\[\\simplify[std]{{odds11}/{odds11+odds12}}+\\simplify[std]{{odds22}/{odds21+odds22}}=\\simplify[std]{{odds11*odds21+odds22*odds12+2*odds11*odds22}/{odds11*odds21+odds22*odds12+odds11*odds22+odds12*odds21}}\\]</p>\n<p>which is less than $1$, as otherwise you could bet on both to win and not lose any money!</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}