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Year 5 Maths

Probability

Explore how likely events are to happen, using chance language and the probability scale from 0 to 1.

Chance Language

We use special words to describe how likely something is to happen. These words sit on a scale from impossible to certain.

The Probability Scale

Impossible
0 Unlikely
  Even Chance
0.5 Likely
  Certain
1
Word Meaning Example
Impossible Will never happen Rolling a 7 on a standard die
Unlikely Probably won't happen Rolling a 6 on a die
Even Chance Equally likely to happen or not Flipping heads on a coin
Likely Will probably happen Picking a red marble from a bag of mostly red marbles
Certain Will definitely happen The sun rising tomorrow

Probability as a Number

We can write probability as a fraction between 0 and 1:

Probability = number of favourable outcomes/total number of possible outcomes

Experiment: Coin Flip

H
T

There are 2 possible outcomes: Heads or Tails.

P(Heads) = 1/2 = 0.5 — this is an even chance.

Experiment: Dice Roll

1
2
3
4
5
6

There are 6 possible outcomes: 1, 2, 3, 4, 5, 6.

P(rolling a 3) = 1/6

P(rolling an even number) = 3/6 = 1/2

Experiment: Spinner

Blue Red Blue Yellow

This spinner has 4 equal sections: 2 Blue, 1 Red, 1 Yellow.

P(Blue) = 2/4 = 1/2    P(Red) = 1/4    P(Yellow) = 1/4

Listing Outcomes

To find probability, you need to list all possible outcomes. Being organised helps you make sure you don't miss any.

Example: Flipping Two Coins

HH

Heads, Heads

HT

Heads, Tails

TH

Tails, Heads

TT

Tails, Tails

There are 4 possible outcomes.

P(both Heads) = 1/4    P(at least one Head) = 3/4

Key Vocabulary

Probability

A measure of how likely an event is to happen, between 0 (impossible) and 1 (certain).

Outcome

A possible result of an experiment (e.g. "Heads" when flipping a coin).

Event

A specific result or set of results that we are interested in (e.g. "rolling an even number").

Experiment

An activity with uncertain results (e.g. rolling a die, flipping a coin).

Worked Examples

1

A bag has 3 red, 2 blue and 5 green marbles. What is the probability of picking a blue marble?

Step 1: Count total marbles: 3 + 2 + 5 = 10

Step 2: Favourable outcomes (blue): 2

Answer: P(blue) = 2/10 = 1/5

2

Is it impossible, unlikely, even chance, likely, or certain that you will roll a number less than 7 on a standard die?

Step 1: A standard die has numbers 1 to 6.

Step 2: Every number (1, 2, 3, 4, 5, 6) is less than 7.

Answer: It is certain (probability = 1).

3

A spinner has 8 equal sections: 5 red and 3 yellow. What is the probability of landing on yellow?

Step 1: Total sections: 8

Step 2: Yellow sections: 3

Answer: P(yellow) = 3/8

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What is the probability of flipping tails on a fair coin?

Question 2

A bag has 4 red balls and 6 blue balls. What is the probability of picking a red ball?

Question 3

Which word describes the chance of rolling an 8 on a standard die?

Question 4

What is the probability of rolling an odd number on a standard die?

Question 5

A spinner has 8 equal sections: 1 green, 2 blue, 5 red. Which colour is most likely to be landed on?

Key Concepts Summary

Year 5: Perimeter Area Volume Year 6: Algebraic Thinking