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A student decides to buy a takeaway. The probability of her choosing pizza is {pizza} and the probability of her choosing hotpot is {hotpot}. If she chooses pizza then the probability that she chooses to drink wine is {wine1}. If she chooses hotpot then the probability that she chooses wine is {wine2}.

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By drawing a tree diagram or otherwise, answer the following questions.

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prob of choosing pizza

", "templateType": "randrange", "can_override": false}, "hotpot": {"name": "hotpot", "group": "Ungrouped variables", "definition": "1-pizza", "description": "", "templateType": "anything", "can_override": false}, "wine1": {"name": "wine1", "group": "Ungrouped variables", "definition": "random(0.2 .. 0.9#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "notwine1": {"name": "notwine1", "group": "Ungrouped variables", "definition": "1-wine1", "description": "", "templateType": "anything", "can_override": false}, "wine2": {"name": "wine2", "group": "Ungrouped variables", "definition": "random(0.2 .. 0.8#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "notwine2": {"name": "notwine2", "group": "Ungrouped variables", "definition": "1-wine2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pizza", "hotpot", "wine1", "notwine1", "wine2", "notwine2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the probability that she chooses pizza and wine?

", "minValue": "pizza*wine1", "maxValue": "pizza*wine1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the probability that she chooses hotpot and also wine?

", "minValue": "hotpot*wine2", "maxValue": "hotpot*wine2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the probability that she does not choose wine?

", "minValue": "pizza*notwine1+hotpot*notwine2", "maxValue": "pizza*notwine1+hotpot*notwine2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}]}]}], "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}]}