What does it mean?
Probability describes chance on a scale from 0 to 1. For a model with equally likely outcomes, divide the number that fit the event by the total number of outcomes. A fair die has six equally likely faces; three are even, so the probability of an even result is 3/6 = 1/2.
For equally likely outcomes, probability is favourable outcomes divided by all possible outcomes. A fair die has six equally likely faces; one is 6, so P(6) = 1/6. An impossible event has probability 0; a certain event has probability 1.
Learning goal: Probability as a fraction. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Fractions if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Describe the event precisely, list the possible outcomes and check that the model makes them equally likely. Count favourable outcomes once each, divide by the total, then simplify. Include 0 for an impossible event and 1 for a certain event. An outcome is what happens once; an event can contain several outcomes.
Notation: probability = favourable outcomes ÷ total equally likely outcomes
Key rule and when to use it
For equally likely outcomes, P(event) = favourable outcomes ÷ all outcomes. Every probability is between 0 and 1 inclusive.
Worked examples, step by step
Example 1: Find the probability of rolling a 6 on a fair die.
- There is 1 favourable face.
- There are 6 equally likely faces.
Answer: 1/6
Example 2: Find the probability of rolling an even number on a fair die.
- The even outcomes are 2, 4 and 6.
- There are 3 favourable outcomes out of 6.
- Simplify 3/6.
Answer: 1/2
Example 3: A bag contains 3 red counters and 5 blue counters. Each counter is equally likely to be drawn. Find P(red).
- There are 3 + 5 = 8 counters in total.
- Three favourable counters are red.
- P(red) = 3/8. P(blue) = 5/8, and the two probabilities add to 1.
Common mistakes and important boundaries
The counting rule needs equal likelihood. Unequal spinner sectors are not equally likely merely because there are four labels. In a bag model, individual objects need an equal chance of selection; their colours do not need equal counts. A probability of 1/2 does not promise exactly half successes in every short experiment.
A point to explain
The numerator counts favourable outcomes, not the number printed on the outcome.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Probability as a Fraction: Equally Likely Outcomes — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
P(tails) on a fair coin = ?
Answer and a way to check
1/2
Count the outcomes that match the event, then count all possible outcomes.
A spinner has 4 equal sections and 1 is red. P(red) = ?
Answer and a way to check
1/4
Count the outcomes that match the event, then count all possible outcomes.
A fair die. P(even) = ?
Answer and a way to check
1/2
Count the outcomes that match the event, then count all possible outcomes.
A fair die. P(7) = ?
Answer and a way to check
0
Count the outcomes that match the event, then count all possible outcomes.
A bag has 1 red apple and 3 green apples. Every apple has an equal chance of being selected. What is the probability of selecting the red apple?
Answer and a way to check
1/4
Count the outcomes that match the event, then count all possible outcomes.
A fair die is rolled. Find P(a number greater than 4).
Answer and a way to check
1/3
Favourable faces are 5 and 6: 2 of 6 equally likely outcomes, giving 2/6 = 1/3.
A spinner has 8 equal sectors, 3 blue. Find P(not blue).
Answer and a way to check
5/8
Five of the eight equally likely sectors are not blue.
A bag holds only 6 green counters. A counter is drawn fairly. Find P(green).
Answer and a way to check
1
Every possible draw is green, so 6/6 = 1.
Probability as a Fraction: Equally Likely Outcomes — answer key
1/2 Count the outcomes that match the event, then count all possible outcomes.
1/4 Count the outcomes that match the event, then count all possible outcomes.
1/2 Count the outcomes that match the event, then count all possible outcomes.
0 Count the outcomes that match the event, then count all possible outcomes.
1/4 Count the outcomes that match the event, then count all possible outcomes.
1/3 Favourable faces are 5 and 6: 2 of 6 equally likely outcomes, giving 2/6 = 1/3.
5/8 Five of the eight equally likely sectors are not blue.
1 Every possible draw is green, so 6/6 = 1.
Questions students and parents ask
Does a fair coin have to alternate heads and tails?
No. Fairness gives a probability of 1/2 for each outcome on an independent toss. Runs such as HHH can occur; they do not force the next toss to be tails.
Does “random” mean every colour has the same chance?
No. With equal-sized counters selected fairly, each counter can have the same chance while a colour appearing on more counters is more likely.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Fractions. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Have your child name the complete list before counting favourable outcomes. Ask what makes the coin, die, spinner or draw fair in the stated model.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Probability as a fraction”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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