// Numbas version: finer_feedback_settings {"name": "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": [{"variable_groups": [], "preamble": {"js": "", "css": ""}, "type": "question", "name": "Probability - Notation and Conversion between Percentages, Decimals and Fractions", "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "showPrecisionHint": true, "strictPrecision": false, "maxValue": "{percentage}/100", "precision": "2", "marks": 1, "scripts": {}, "minValue": "{percentage}/100", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}, {"correctAnswerFraction": true, "mustBeReduced": true, "type": "numberentry", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": true, "scripts": {}, "minValue": "{percentage}/100", "maxValue": "{percentage}/100", "marks": 1, "variableReplacements": []}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "

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

Convert this probability to a decimal.

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

ii)

Convert this probability to a fraction.

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

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

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

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

ii)

Convert this probability to a fraction.

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

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The probability that a football match between Newcastle United and Manchester United ends in a draw is $\\displaystyle\\frac{1}{\\var{denominator}}$.

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

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

ii)

Convert this probability to a decimal.

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

"}], "advice": "

a)

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

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

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

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

ii)

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

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

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

b)

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

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

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

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

ii)

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

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

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

c)

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

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

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

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

ii)

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

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

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

", "tags": ["conversion", "Decimals", "decimals", "fractions", "Fractions", "percentages", "Probability", "probability", "taxonomy"], "variables": {"percentage": {"templateType": "anything", "description": "

Part a.

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Part c.

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Part b.

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Probabilities can be expressed as fractions, decimals or percentages.

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

", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

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

"}, "extensions": [], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}]}