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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.

#### 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.

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\$\\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 $\\mathrm{P}(\\text{Late}) = \\var{decimal}$.

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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 $\\displaystyle\\frac{100}{100}$.

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

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#### 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} \

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

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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).

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

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Part b.

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Part a.

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Part c.

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

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i)

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Convert this probability to a decimal.

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

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ii)

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Convert this probability to a fraction.

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

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

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i)

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

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

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ii)

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Convert this probability to a fraction.

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

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