D. Data · Data Literacy and Probability

Probability as Fractions, Decimals and Percents

D2.1About 50 minutes

Learning goals

I can write the probability of an event as a fraction, a decimal and a percent.
I can show probabilities on a probability line from 0 (0%) to 1 (100%).
I can use probability to make predictions and informed decisions.

Words to know

probability
A number from 0 to 1 (or 0% to 100%) that tells how likely an event is.

outcome
One possible result, like rolling a 4.

event
One outcome or a group of outcomes you are interested in, like rolling an even number.

equally likely
Having the same chance of happening.

percent
Out of 100. 35% means 35 out of 100, or 0.35.

Remember from Grade 5

When all the outcomes are equally likely:

probability of an event = number of favourable outcomes ÷ total number of outcomes

You wrote probabilities as fractions on a probability line from 0 (impossible) to 1 (certain). This year you'll also write them as decimals and percents.

Three ways to say the same chance

Spinner A has 10 equal sections: 5 green, 3 yellow and 2 blue.

P(green) = 5/10 = 0.5 = 50%
P(yellow) = 3/10 = 0.3 = 30%
P(blue) = 2/10 = 0.2 = 20%

"P(green)" is a short way to write "the probability of green".

A percent means "out of 100". To change a fraction to a percent, make an equivalent fraction with a denominator of 100: 3/10 = 30/100 = 30%. The decimal is the same number of hundredths: 0.30, or 0.3.

The probabilities of all the outcomes add up to 1, or 100%: 50% + 30% + 20% = 100%.

Spinner A: 10 equal sections. Five are green, three are yellow and two are blue.

Spinner A's probabilities on a probability line: blue at 0.2 (20%), yellow at 0.3 (30%), green at 0.5 (50%).

Reading the probability line

0 or 0%: impossible (spinning red on Spinner A).
Less than 1/2 or 50%: unlikely (blue, yellow).
1/2 or 50%: equally likely to happen or not happen (green).
More than 50%: likely.
1 or 100%: certain (spinning green, yellow or blue).

🟢🟢🟢🟢🟢🟢🟢🟡🟡🟡🟡🟡🟡🟡🟡🔵🔵🔵🔵🔵

A bag holds 20 counters: 7 green, 8 yellow and 5 blue.

Worked example

Example 1: Fraction, decimal and percent

You pick one counter from the bag without looking. Find P(green), P(yellow) and P(blue) as fractions, decimals and percents.

There are 7 + 8 + 5 = 20 counters, all equally likely to be picked.
P(green) = 7/20. Multiply top and bottom by 5 to get hundredths: 7/20 = 35/100 = 0.35 = 35%.
P(yellow) = 8/20 = 40/100 = 0.40 = 40%.
P(blue) = 5/20 = 25/100 = 0.25 = 25%.
Check: 35% + 40% + 25% = 100%. ✓

Green 7/20 = 0.35 = 35%, yellow 8/20 = 0.4 = 40%, blue 5/20 = 0.25 = 25%.

Worked example

Example 2: Make a prediction

You pick a counter, record its colour and put it back. You do this 60 times. About how many times do you expect to pick green?

P(green) = 35% = 0.35.
Expected number = probability × number of trials = 0.35 × 60.
0.35 × 60: 0.35 × 10 = 3.5, so 0.35 × 60 = 3.5 × 6 = 21.
It's a prediction, not a promise. You might get 18 or 24 greens, but about 21 is the best guess.

About 21 times.

Worked example

Example 3: Make an informed decision

In a game, you win if you get yellow. You can either spin Spinner A once or pick one counter from the bag. Which should you choose?

Spinner A: P(yellow) = 3/10 = 30%.
Bag: P(yellow) = 8/20 = 40%.
40% is greater than 30%, so the bag gives a better chance.

Pick from the bag: a 40% chance of winning instead of 30%.

Probability in real life

Weather forecasts often give a percent for the chance of rain or snow, like "70% chance of snow tomorrow." That means snow is likely, but not certain. An informed decision might be: "I'll wear my boots and bring snow pants."

Just for fun

Weather forecast: "50% chance of snow tomorrow."

Translation: it will snow... or it won't. Better bring your boots just in case!

Hands-on activity

Ten-section spinner

You need: paper, a pencil, a ruler, pencil crayons in three colours, and a paper clip.

Trace around a round lid or plate to draw a circle. Divide it into 10 equal sections. (Draw a line through the centre to make halves, then split each half into 5 equal parts. Do your best: it helps to estimate with a ruler.)
Colour the sections in three colours, any way you like (for example 6, 3 and 1).
For each colour, write the probability as a fraction, decimal and percent. Check that they add to 100%.
Mark each colour on a probability line from 0 to 1 (0% to 100%).
Predict how many times each colour will come up in 50 spins. Spin by holding a pencil point in the centre through the paper clip and flicking the clip. Record and compare with your predictions.

Your turn

A bag has 4 red marbles and 16 white marbles. Find P(red) as a fraction, decimal and percent.

Same bag: find P(white) as a percent.

A regular die is rolled. Find P(rolling a 5).

A regular die is rolled. Find P(an even number) as a fraction, decimal and percent.

Spinner A: what is P(not blue)?

Spinner A is spun 200 times. About how many times do you expect yellow?

Place these on a probability line from 0 to 1: P(spinning purple on Spinner A), P(green), P(rolling a number less than 7 on a die).

More practice: warm-up

Write 1/4 as a decimal and a percent.

Write 0.6 as a fraction and a percent.

What percent means certain?

What percent means impossible?

A coin is flipped. What is P(heads) as a percent?

More practice: on your own

A standard deck of 52 cards has 13 hearts. What is P(heart) as a fraction, decimal and percent?

Same deck: half the cards are red. What is P(black)?

A bag has 3 green, 5 yellow and 2 blue tiles. Which colour has a probability of 50%?

The forecast says 30% chance of snow. What is the chance of no snow? Is snow likely or unlikely?

You pick from the bag of 20 counters (7 green, 8 yellow, 5 blue) 100 times, putting the counter back each time. Predict the number of each colour.

Challenge

Design a bag of 20 marbles in three colours so that P(red) = 45%, P(white) = 0.35 and P(black) = 1/5.

A spinner has 8 equal sections. P(win) is 37.5%. How many sections say WIN? Explain.

Game 1: roll a die and win on a 1 or 2. Game 2: spin Spinner A and win on blue. Game 3: pick a card from a full deck and win on a heart. Order the games from best to worst chance of winning, using percents.

Check your understanding

Quiz

What is 3/4 as a percent?

A bag has 2 green and 8 yellow tiles. What is P(green)?

Where does a probability of 0.5 go on the probability line?

P(snow) = 85%. What is P(no snow)?

P(green) = 0.35. In 100 picks (with replacement), about how many greens would you expect?

Which shows the same probability?

For parents and teachers

What this lesson teaches: writing probabilities as fractions, decimals and percents (percents are new in Grade 6 probability), showing them on a probability line from 0 to 1 (0% to 100%), and using them to make predictions and informed decisions (D2.1).

How to help at home:

Use weather forecasts: "40% chance of rain: likely or unlikely? What's the chance of no rain?"
Practise converting with tenths and hundredths first (3/10 = 30%, 7/20 = 35/100 = 35%).
Use a deck of cards, dice or coloured objects to make probabilities concrete.

Common difficulties:

Writing 0.4 as 4% instead of 40%.
Forgetting that outcomes must be equally likely before dividing (a spinner with unequal sections can't be counted section by section).
Treating a prediction as a promise: expecting exactly 21 greens in 60 picks.