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Year 6 Maths Chance

Order chance words on a 0-1 scale

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Theory

The chance of an event can be shown on a scale from 0 to 1. An impossible event has probability \(0\), a certain event has probability \(1\), and an event with an even chance sits at \(\dfrac{1}{2}\). This Year 6 maths page shows how to match chance words to the scale and order events from least to most likely.

The probability of an event is a number from \(0\) to \(1\) that tells how likely it is.

Impossible \(= 0\): it cannot happen. Certain \(= 1\): it must happen. Even chance \(= \dfrac{1}{2}\): just as likely to happen as not.

Unlikely events are between \(0\) and \(\dfrac{1}{2}\). Likely events are between \(\dfrac{1}{2}\) and \(1\).

When all outcomes are equally likely, compare how many outcomes give the event with how many there are altogether. On a spinner with \(8\) equal sectors, \(5\) green sectors make green likely (\(\dfrac{5}{8}\) is more than a half).

Probability scale with chance words A scale from 0 to 1 marked 0, one quarter, one half, three quarters and 1, with the words impossible, unlikely, even chance, likely and certain underneath. Point A is at 0, point B at one half and point C at seven eighths. 0 1/4 1/2 3/4 1 impossible unlikely even chance likely certain less likely ← → more likely A B C
A is impossible, B is an even chance, C is likely (close to certain).
Spinner with five green and three yellow sectors A spinner with eight equal sectors: five green and three yellow. green yellow green green yellow green yellow green
Green: \(5\) of \(8\) sectors, likely. Yellow: \(3\) of \(8\), unlikely.
Bag of two red and six blue counters A bag holding eight counters: two red and six blue.
Red: \(2\) of \(8\) (unlikely). Blue: \(6\) of \(8\) (likely).

Chance words and their place on the scale:

Chance wordProbability
impossible\(0\)
unlikelybetween \(0\) and \(\dfrac{1}{2}\)
even chance\(\dfrac{1}{2}\)
likelybetween \(\dfrac{1}{2}\) and \(1\)
certain\(1\)
\[ 0 \le \text{probability} \le 1 \]
0 probability 1
More outcomes, more likely. With equal sectors or equal counters, the colour with more of them is more likely.
Two outcomes is not always even. Win or lose are two outcomes, but they are only an even chance if they are equally likely.

How to place an event on the scale

  1. Ask: can it happen at all? If not, it is at \(0\). Must it happen? Then it is at \(1\).
  2. Count the outcomes that give the event and the total number of equally likely outcomes.
  3. Compare with half: less than half is unlikely, exactly half is even chance, more than half is likely.
Example 1 — Impossible or certain
Describe each event.
(i) A month has \(32\) days.
(ii) A letter taken from a bag holding only A, E and O tiles is a vowel.
Solution

(i) Impossible (probability \(0\))
(ii) Certain (probability \(1\))

Example 2 — Even chance
A die is rolled. Which chance word describes rolling an odd number?
Solution

Odd numbers: \(1, 3, 5\). That is \(3\) of the \(6\) outcomes, exactly half.

Even chance.

Example 3 — Unlikely
A die is rolled. Describe rolling a \(5\) or a \(6\).
Solution

\(2\) of the \(6\) outcomes, which is less than half.

Unlikely.

Example 4 — Spinner
Use the spinner diagram.
(i) Which colour is more likely?
(ii) Describe landing on yellow.
Solution

(i) Green (\(5\) sectors against \(3\))
(ii) Unlikely, but possible

Example 5 — Read the scale
Use the probability scale. Which point could show:
(i) a fair coin landing tails?
(ii) a spinner landing on one of \(7\) red sectors out of \(8\)?
(iii) rolling a \(9\) on a normal die?
Solution

(i) B
(ii) C
(iii) A

Example 6 — Bag of counters
A bag holds \(2\) red and \(6\) blue counters. One is drawn without looking. Describe drawing red and drawing blue.
Solution

Red: unlikely (\(2\) out of \(8\)). Blue: likely (\(6\) out of \(8\)).

Example 7 — Which bag is better?
Bag A has \(3\) orange and \(7\) purple marbles. Bag B has \(5\) orange and \(5\) purple. Which bag gives the better chance of orange?
Solution

Bag B: orange is an even chance there, but unlikely in bag A (\(3\) out of \(10\)).

Example 8 — Order events
Order from least likely to most likely: P: rolling a number less than \(5\) on a die; Q: a coin landing heads; R: rolling a \(1\) on a die.
Solution

R: \(1\) of \(6\). Q: half. P: \(4\) of \(6\), more than half.

R, Q, P.

Example 9 — Find the mistake
A spinner has \(5\) equal sectors: \(1\) says WIN and \(4\) say LOSE. Ella says "It is an even chance, because I either win or lose." What is right?
Solution

Win and lose are not equally likely. Win is \(1\) sector of \(5\), so winning is unlikely.

Common pitfalls

Two outcomes means even chance. Only if the two outcomes are equally likely.
Calling unlikely events impossible. Unlikely events can still happen; only impossible events have probability 0.
Putting numbers above 1 on the scale. Probabilities are never less than 0 or more than 1.
Comparing counts from different-sized bags. \(5\) out of \(10\) and \(3\) out of \(10\) compare easily; always think of the fraction of the bag.

Frequently asked questions

What numbers are at the two ends of the chance scale?

\(0\) for impossible and \(1\) for certain.

Where is even chance on the scale?

Exactly halfway, at \(\dfrac{1}{2}\).

Where do unlikely events go?

Between \(0\) and \(\dfrac{1}{2}\).

How do I decide if an event is likely?

Compare the outcomes that give the event with the total: more than half means likely.

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