// Numbas version: exam_results_page_options {"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": [{"tags": ["conversion", "Decimals", "decimals", "fractions", "Fractions", "percentages", "Probability", "probability", "taxonomy"], "statement": "

Probabilities can be expressed as fractions, decimals or percentages.

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

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

Part a.

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Part b.

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Part c.

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

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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]]

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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).

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