🎲 Probability

From impossible to certain – measure the chance of any event!

📖 Learn
Probability concepts

✏️ Examples
Worked problems

🔬 Visualiser
Interactive tools

🎯 Practice
20 mixed questions

📖 Probability

1. Probability Language

We describe probability using words on a scale from impossible to certain.

Impossible → Unlikely → Even Chance → Likely → Certain
0 ————————— 0.5 ————————— 1

Word	Meaning	Example
Impossible	P = 0, cannot happen	Roll a 7 on a standard die
Unlikely	P is less than 0.5	Roll a 1 on a die (P = 1/6)
Even chance	P = 0.5, equally likely either way	Flip heads on a fair coin
Likely	P is more than 0.5	Roll a number > 1 on a die
Certain	P = 1, will definitely happen	Sun rises tomorrow

2. Probability as a Fraction

Probability is calculated by counting favourable outcomes divided by total equally likely outcomes.

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

Example: Probability of rolling a 3 on a die = 1 ÷ 6 = 1/6

Example: Probability of picking red from {R, R, G, B, B} = 2 ÷ 5 = 2/5

3. Probability as a Decimal and Percentage

Probability fractions can be converted to decimals and percentages.

P = fraction → divide → decimal → × 100 → percentage

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%

4. The Complement Rule

The probability of an event NOT happening is called the complement.

P(not A) = 1 − P(A)

Example: P(rain) = 1/3 → P(no rain) = 1 − 1/3 = 2/3

The event and its complement always add up to exactly 1.

5. Listing Outcomes (Sample Space)

A sample space is a list of all possible outcomes. We list them systematically to avoid missing any.

Total outcomes for two independent events = outcomes₁ × outcomes₂

Coin (H/T) × Die (1–6) = 2 × 6 = 12 outcomes

Two coins: HH, HT, TH, TT = 4 outcomes

Two dice: 6 × 6 = 36 outcomes

✏️ Worked Examples

Example 1 – Probability as a Fraction

A bag contains 3 red, 2 blue and 5 green balls. What is the probability of picking a red ball?

Step 1: Count favourable outcomes → 3 red balls

Step 2: Count total outcomes → 3 + 2 + 5 = 10 balls

Step 3: P(red) = 3/10 = 0.3 = 30%

Example 2 – Complement Rule

P(win a raffle) = 3/20. What is the probability of NOT winning?

Step 1: Use complement rule → P(not win) = 1 − P(win)

Step 2: P(not win) = 1 − 3/20 = 20/20 − 3/20

Step 3: P(not win) = 17/20

Example 3 – Converting Probability

P(heads) = 1/2. Express as a decimal and percentage.

Step 1: Fraction to decimal → 1 ÷ 2 = 0.5

Step 2: Decimal to percentage → 0.5 × 100 = 50%

Example 4 – Listing Outcomes

A coin is flipped and a die is rolled. How many different outcomes are possible? List them systematically.

Step 1: Coin outcomes: H, T (2 outcomes)

Step 2: Die outcomes: 1, 2, 3, 4, 5, 6 (6 outcomes)

Step 3: Total = 2 × 6 = 12 outcomes
H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

🔬 Probability Visualiser

Probability Calculator

Favourable outcomes:

Total outcomes:

Complement Finder

Enter P(A) as a fraction:

Numerator:

Denominator:

Coin Flip Simulator

Press to flip! Tracks your results.

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Exercise 1 – Probability Language

Enter a number: 0 = impossible, 1 = unlikely, 2 = even chance, 3 = likely, 4 = certain

Exercise 2 – Probability as a Fraction

Give the numerator of the probability fraction (denominator shown in question).

Exercise 3 – Complement Rule

Give the numerator of P(not A) (denominator shown in question).

Exercise 4 – Probability as Decimal/Percentage

Convert each probability as shown (decimal or %).

Exercise 5 – Sample Spaces & Outcomes

Count outcomes or give probabilities.