What is the probability that both of these events occur?
", "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "{x}*{y}"}, {"strictPrecision": false, "useCustomName": false, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "allowFractions": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "precision": "2", "customName": "", "showPrecisionHint": false, "precisionPartialCredit": 0, "marks": "2", "customMarkingAlgorithm": "", "minValue": "(1-{x})*(1-{y})", "variableReplacements": [], "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "prompt": "What is the probability that neither of these events occur?
", "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "(1-{x})*(1-{y})"}, {"strictPrecision": false, "useCustomName": false, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "allowFractions": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "precision": "2", "customName": "", "showPrecisionHint": false, "precisionPartialCredit": "0", "marks": "2", "customMarkingAlgorithm": "", "minValue": "1-(1-{x})*(1-{y})", "variableReplacements": [], "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "prompt": "What is the probability that at least one of these two events will occur?
", "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "1-(1-{x})*(1-{y})"}, {"strictPrecision": false, "useCustomName": false, "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "allowFractions": false, "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst", "precision": "2", "customName": "", "showPrecisionHint": false, "precisionPartialCredit": 0, "marks": "2", "customMarkingAlgorithm": "", "minValue": "(1-{x})*{y}+(1-{y})*{x}", "variableReplacements": [], "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "prompt": "What is the probability that only one of the two events occur?
", "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "(1-{x})*{y}+(1-{y})*{x}"}], "ungrouped_variables": ["y", "thing", "x", "a1d", "a2", "a3", "a4", "a1", "a2d", "a3d", "a4d"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "rebelmaths
"}, "name": "Simon's copy of Simon's copy of Probability independent", "rulesets": {}, "statement": "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 two decimal places.
", "variable_groups": [], "advice": "Let
\nA = {thing[0]}
\nand
\nB = {thing[1]}
\n\n(a)
\nSince the events are independent, we can calculate
\nP(A and B) = P(A) $\\times$ P(B) = $\\var{x} \\times \\var{y}=\\var{a1}$
\nNext round to 2 decimal places to get {precround(a1d,2)}
\n\n(b)
\nP(neither A nor B)=P(not A AND not B)= P(not A) $\\times$ P(not B)$=(1-\\var{x})\\times (1-\\var{y})=\\var{a2}$
\nNext round to 2 decimal places to get {a2d}
\n\n(c)
\nP(at least one of A or B occurs) = 1 - P(neither A nor B) = 1 - {a2d} = {a3d} using the answer from part (b)
\n\n
(d)
\nP(only one of A or B occurs) = P(A occurs and B doesn't OR B occurs and A doesn't)
\n= P(A and not B) + P(B and not A)
\n= $ \\var{x} \\times (1-\\var{y}) + \\var{y} \\times (1-\\var{x})=\\var{a4}$
\nNext round to 2 decimal places to get {precround(a4d,2)}
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