// Numbas version: finer_feedback_settings {"name": "Maria's copy of Probability - Notation and Conversion between Percentages, Decimals and Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

Probabilities can be expressed as fractions, decimals or percentages.

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Convert each of the following probabilities into each of the two alternative numerical forms. 

", "advice": "

a)

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We are told that $\\mathrm{P}(\\text{Rain}) = \\var{percentage}\\%$.

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i)

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To convert this to a decimal, we divide $\\var{percentage}$ by $100$.

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\\[\\frac{\\var{percentage}}{100} = \\simplify{{{percentage}/100}}.\\]

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Then, $\\mathrm{P}(\\text{Rain}) = \\simplify{{{percentage}/100}}$.

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ii)

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Similary, to convert this to a fraction, we divide $\\var{percentage}$ by $100$, but leave the fraction in its simplified form.

\n

\\[\\frac{\\var{percentage}}{100} = \\simplify{{percentage}/100}.\\]

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Then, $\\mathrm{P}(\\text{Rain}) = \\displaystyle\\simplify{{percentage}/100}$.

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b)

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We are told that $\\mathrm{P}(\\text{Late}) = \\var{decimal}$.

\n

i)

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To convert this to a percentage, we multiply $\\var{decimal}$ by $100$.

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\\[\\var{decimal} \\times 100 = \\simplify{{decimal}*100}.\\]

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Then, $\\mathrm{P}(\\text{Late}) = \\simplify{{decimal}*100}\\%$.

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ii)

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To convert this to a fraction, we multiply $\\var{decimal}$ by $\\displaystyle\\frac{100}{100}$. 

\n

\\[
\\begin{align}
\\var{decimal} \\times \\frac{100}{100} &= \\frac{\\simplify{{decimal}*100}}{100} \\\\[0.5em]
&= \\simplify{({decimal*100})/100}.
\\end{align}
\\]

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Then, $\\mathrm{P}(\\text{Late}) =\\displaystyle\\simplify{({decimal}*100)/100}$.

\n

c)

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We are told that $\\mathrm{P}(\\text{Draw}) = \\displaystyle\\frac{1}{\\var{denominator}}$.

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i)

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To convert this to a percentage, we multiply $\\displaystyle\\frac{1}{\\var{denominator}}$ by $100$.

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\\[
\\begin{align}
\\frac{1}{\\var{denominator}} \\times 100 &= \\var{100/{denominator}} \\\\
&= \\var{dpformat(100/{denominator},0)} & (\\text{rounded to the nearest integer}).
\\end{align}
\\]

\n

So, $\\mathrm{P}(\\text{Draw}) = \\var{dpformat(100/{denominator},0)}\\%$.

\n

ii)

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To convert this to a decimal, we can use a calculator to calculate $1 \\div \\var{denominator}$.

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\\[\\frac{1}{\\var{denominator}} = \\simplify{{1/{denominator}}}.\\]

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So, $\\mathrm{P}(\\text{Draw}) = \\var{dpformat(1/{denominator},2)}$ (rounded to two decimal places).

", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Represent a given probability to a decimal, fraction or percentage.

"}, "ungrouped_variables": ["percentage", "decimal", "denominator"], "variable_groups": [], "variables": {"decimal": {"templateType": "anything", "group": "Ungrouped variables", "description": "

Part b.

", "name": "decimal", "definition": "random(0.10..0.90 #0.10 except percentage/100 )"}, "percentage": {"templateType": "anything", "group": "Ungrouped variables", "description": "

Part a.

", "name": "percentage", "definition": "random(10..90 #10)"}, "denominator": {"templateType": "anything", "group": "Ungrouped variables", "description": "

Part c.

", "name": "denominator", "definition": "random(3..9 except 5) "}}, "extensions": [], "preamble": {"js": "", "css": ""}, "parts": [{"gaps": [{"mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{percentage}/100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "useCustomName": false, "showPrecisionHint": true, "scripts": {}, "correctAnswerStyle": "plain", "marks": "0.25", "showFeedbackIcon": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "precisionType": "dp", "unitTests": [], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "minValue": "{percentage}/100", "customName": "", "variableReplacements": [], "precisionPartialCredit": 0, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "precision": "2"}, {"notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "maxValue": "{percentage}/100", "showFractionHint": true, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "scripts": {}, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "marks": "0.25", "customName": "", "showFeedbackIcon": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "correctAnswerFraction": true, "showCorrectAnswer": true, "variableReplacements": [], "minValue": "{percentage}/100", "mustBeReduced": true, "unitTests": []}], "prompt": "

The probability that it rains today is $\\var{percentage}\\%$.

\n

i)

\n

Convert this probability to a decimal.

\n

$\\mathrm{P}(\\text{Rain}) =$ [[0]]

\n

ii)

\n

Convert this probability to a fraction.

\n

$\\mathrm{P}(\\text{Rain}) =$ [[1]]

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The probability that your bus is late today is $\\var{decimal}$.

\n

i)

\n

Convert this probability to a percentage (if necessary, round your answer to the nearest percent).

\n

$\\mathrm{P}(\\text{Late}) =$ [[0]]$\\%$.

\n

ii)

\n

Convert this probability to a fraction.

\n

$\\mathrm{P}(\\text{Late}) =$ [[1]]

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