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Probabilities as Rational Number


We've already looked at how probabilities are used to describe the chance of an event happening. Words such as "impossible," "certain," or "even chance" describe the likelihood of an event.

Now let's look at how we can use maths and numbers to describe probabilities as well.


Flipping a Coin


Let's say we flipped a coin. What outcomes are possible? In other words, what can the coin land on?



It can either land on heads or tails. In other words, there is an even chance of the coin landing on heads or tails because the chance of it landing on heads is the same as landing on tails.

So what is the probability that when we flip the coin, we get a head?

Well there is a $1$1 out of $2$2 chance of that happening, so we can write the probability of getting a head:

  • as a fraction: $\frac{1}{2}$12
  • as a decimal: $0.5$0.5
  • or as a percentage: $50%$50%

Probability can be expressed as a fraction, decimal or percentage, so make sure you're comfortable converting between these forms.


Spin the Spinner

Let's say we spun this spinner. What outcomes are possible? Are the chances of landing on each colour equal?

Well we could land on green, blue, red and yellow but the chances of doing so aren't equal.


Just because there a $4$4 colours doesn't mean the chances of landing on each one are equal ($\frac{1}{4}$14). The green section is bigger, so the probability of landing on it is greater. Similarly, the red section is smaller, so the probability of landing on it is smaller. 

So what is the probability of landing on red?

Well, the picture shows $8$8 equal pieces. $1$1 of those is coloured red, so the probability of landing on red is $\frac{1}{8}$18

Now it's your turn!

Practice writing probabilities as fractions with this applet.

Discuss your answers and how you would express these probabilities in words (Certain, likely, even chance, unlikely or impossible).


Question 1

Homer has a bag of marbles with $10$10 marbles. $8$8 of those marbles are red.

Express the chance of Homer picking a red marble as a decimal.

Think: There is an $8$8 out of $10$10 chance Homer will pick a red marble.

Do: $8$8 out of $10$10 is the same as $\frac{8}{10}$810 or "$8$8 tenths." As a decimal, we would write this as $0.8$0.8


Question 2

A coin was tossed $50$50 times. It landed on tails $5$5 times.

Write the probability of getting as tail as a percentage.

Think: How do we write $5$5 out of $50$50 as a percentage?

Do: "Percentage" means "out of $100$100," so let's work out this probability out of $100$100.

$5$5 out of $50$50 $=$= $\frac{5}{50}$550 (Multiply the fraction by $2$2 to change the denominator to $100$100)
  $=$= $\frac{10}{100}$10100 (Now convert to a percentage)
  $=$= $10%$10%  

Worked Examples


The spinner below is spun.

  1. Express the chance it lands on blue as a fraction in its simplest form.

  2. Express the chance it lands on blue as a percentage.

  3. Express the probability of landed on blue as a decimal.


A coin was tossed $50$50 times. It landed on tails $4$4 times. Each toss was recorded.

  1. Out of these tosses, what is the probability of selecting one that landed on tails? Write this probability as a decimal.


A die is rolled $100$100 times. The results are shown in the table.

Result Frequency
$1$1 $14$14
$2$2 $12$12
$3$3 $11$11
$4$4 $13$13
$5$5 $14$14
$6$6 $36$36
  1. Express the chance it lands on $five$five as a fraction.

  2. Express the chance it lands on $five$five as a decimal.

  3. Express the chance it lands on $five$five as a percentage.

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