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15. Probability
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Stage 3

15.05 Probability with decimals and percentages

Lesson
Practice
Lesson

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Can you  convert  a fraction to a decimal and percentage? When finding a probability as a decimal or percentage, we can first find the  probability as a fraction  and then convert.

Examples

Example 1

Convert between percentages, fractions and decimals to complete the table:

FractionDecimalPercentage
\dfrac{60}{100}
Worked Solution
Create a strategy

To convert fractions and decimals to percentages multiply by 100\%.

Apply the idea

To convert the fraction to a percentage:

\displaystyle \dfrac{60}{100}\displaystyle =\displaystyle \dfrac{60}{100} \times 100\%Multiply by 100\%
\displaystyle =\displaystyle 60\%Cancel out the 100s

To convert the fraction to a decimal:

\displaystyle \dfrac{60}{100}\displaystyle =\displaystyle \dfrac{6}{10}Simplify the fraction
\displaystyle =\displaystyle 0.6Write 6 tenths as a decimal
FractionDecimalPercentage
\dfrac{60}{100}0.660\%
Idea summary

To convert fractions and decimals to percentages multiply by 100\%.

To convert decimals to percentages multiplying by 100\% is the same as increasing the place value of each digit by two places, and attaching a \% symbol.

Probability with decimals

Let's see how we can express the probability of something happening in decimals.

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Examples

Example 2

A box of star stickers has 6 purple stickers, 4 blue stickers and 10 black stickers.

a

Complete the following table showing the probability of randomly selecting each colour:

OutcomeProbabilty (Fraction)Probability (Decimal)
\text{Purple}\dfrac{3}{10}0.3
\text{Blue}\dfrac{1}{5}
\text{Black}\dfrac{1}{2}
Worked Solution
Create a strategy

Convert each fraction to a decimal.

Apply the idea

To convert \dfrac{1}{5} and \dfrac{1}{2} to decimals we must first convert them to fractions out of 10.

\displaystyle \dfrac{1}{5}\displaystyle =\displaystyle \dfrac{1\times 2}{5\times 2}Multiply both parts by 2
\displaystyle =\displaystyle \dfrac{2}{10}
\displaystyle =\displaystyle 0.2Write 2 tenths as a decimal
\displaystyle \dfrac{1}{2}\displaystyle =\displaystyle \dfrac{1\times5}{2\times5}Multiply both parts by 5
\displaystyle =\displaystyle \dfrac{5}{10}
\displaystyle =\displaystyle 0.5Write 5 tenths as a decimal
OutcomeProbabilty (Fraction)Probability (Decimal)
\text{Purple}\dfrac{3}{10}0.3
\text{Blue}\dfrac{1}{5}0.2
\text{Black}\dfrac{1}{2}0.5
b

What is the sum of the probabilities for each outcome?

Worked Solution
Create a strategy

Add the probabilities in the last column.

Apply the idea
\displaystyle \text{Sum}\displaystyle =\displaystyle 0.3+0.2+0.5Add the probabilities
\displaystyle =\displaystyle 1
Idea summary

To convert a fraction to a decimal where the denominator is not a power of 10:

  1. Find a suitable number to multiply or divide the denominator by to make it a power of 10.

  2. Multiply or divide both the numerator and denominator by this number.

  3. Write the number in decimal form.

Probability with percentages

We can also work out the probability of something happening using percentages. We'll use a calculator to help us this time.

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Examples

Example 3

The spinner below is spun.

The image shows a spinner with 10 sectors. 3 are red, 4 are blue, 1 is yellow and 2 are green.
a

What is the chance it lands on blue? Write your answer as a fraction in its simplest form.

Worked Solution
Create a strategy

The chance (probability) can be calculated by: \dfrac{\text{Number of blue parts}}{\text{Total number of parts}}

Apply the idea

There are 4 blue parts out of 10 parts.

\displaystyle \text{Probability}\displaystyle =\displaystyle \dfrac{4}{10}Substitute the number of parts
\displaystyle =\displaystyle \dfrac{4 \div 2}{10 \div 2}Divide both parts by 2
\displaystyle =\displaystyle \dfrac{2}{5}Simplify the fraction
b

What is the chance it lands on blue as a percentage?

Worked Solution
Create a strategy

Multiply both parts of the fraction, found in part (a), by a number that will make the denominator 100.

Apply the idea

5\times 20 = 100, so we need to multiply the numerator and denominator by 20.

\displaystyle \dfrac{2}{5}\displaystyle =\displaystyle \dfrac{2\times 20}{5\times 20}Multiply both parts by 20
\displaystyle =\displaystyle \dfrac{40}{100}
\displaystyle =\displaystyle \dfrac{40}{100} \times 100\%Multiply by 100\%
\displaystyle =\displaystyle 40\%Cancel out the 100s
c

What is the chance it lands on blue as a decimal?

Worked Solution
Create a strategy

Use a place value table to write the decimals.

Apply the idea

40 \% is the same as \dfrac{40}{100}. To put it in a place value table, put the 0 in the hundredths column, 4 in the tenths column, and use a 0 for a placeholder:

Unit.TenthsHundredths
0.40

\text{Probability}=0.4

Idea summary

Decimals and percentages are another way to express numbers, so we can use them for probability as well. If something is unlikely, and only has a one in four chance of happening \left(\dfrac{1}{4}\right), we may wish to express the probability of it happening as 0.25 or 25\%.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

MA3-19SP

conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

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