🎲 Probability

Describe chance, calculate probabilities and predict outcomes!

📖 Learn
Chance and probability

✏️ Examples
Worked problems

🔬 Visualiser
Probability tools

🎯 Practice
20 mixed questions

📖 Probability

1. Probability Scale (0 to 4 scale)

0 Impossible

1 Unlikely

2 Even chance

3 Likely

4 Certain

0 = will never happen | 4 = will definitely happen | 2 = equal chance either way

2. Simple Probability Fractions

P(event) = number of favourable outcomes ÷ total outcomes

Example: Bag with 2 red and 3 blue → P(red) = 2/5

Probability is always between 0 (impossible) and 1 (certain).

3. Complement

The complement is the probability of an event NOT happening.

P(not A) = 1 − P(A)

If P(red) = 2/5, then P(not red) = 1 − 2/5 = 3/5

P(A) + P(not A) = 1 always

4. Sample Spaces

A sample space is the list of all possible outcomes.

Experiment	Sample space	Total outcomes
Coin flip	H, T	2
Roll a die	1,2,3,4,5,6	6
2 coin flips	HH,HT,TH,TT	4

5. Expected Frequency

If you repeat an experiment many times, you can predict roughly how often an event will occur.

Expected frequency = probability × number of trials

Example: P(head) = 1/2, flip 60 times → expected heads = 1/2 × 60 = 30

✏️ Worked Examples

Example 1 – Probability scale

Describe the probability of rolling a 7 on a standard die (0–4 scale).

A standard die has faces 1–6. There is no 7.

This is impossible.

Answer: 0

Example 2 – Probability fraction

A bag has 3 red and 5 blue balls. What is P(blue)?

Favourable outcomes = 5 (blue)

Total outcomes = 3 + 5 = 8

P(blue) = 5/8 → numerator = 5

Example 3 – Complement

P(win) = 1/4. What is P(not win)?

P(not win) = 1 − P(win) = 1 − 1/4 = 3/4

Numerator = 3

Example 4 – Expected frequency

A spinner has 3 equal sections. Spin 60 times. How many times do you expect section 1?

P(section 1) = 1/3

Expected = 1/3 × 60 = 20

🔬 Probability Tools

Probability Calculator

Favourable outcomes:

Total outcomes:

Complement Calculator

P(A) numerator:

P(A) denominator:

Expected Frequency

P numerator:

P denominator:

Number of trials:

Probability Scale

Exercise 1 – Probability Scale (0=Impossible, 1=Unlikely, 2=Even, 3=Likely, 4=Certain)

Rate each event on the 0–4 scale.

Exercise 2 – Probability Fraction (give the numerator)

Write the numerator of the probability fraction. Denominator is given.

Exercise 3 – Complement (give numerator of complement)

Find the numerator of P(not A).

Exercise 4 – Sample Spaces

Count the outcomes in each sample space.

Exercise 5 – Word Problems

Solve each probability problem.