Probability

Basic Probability

Probability measures how likely an event is. It is always between 0 and 1 (or 0% and 100%).

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

Example: A bag has 3 red, 5 blue and 2 green marbles. P(red) = 3/10 = 0.3 = 30%

Sample Space & Complementary Events

The sample space is the list of all possible outcomes.

Example: Rolling a die: sample space = {1, 2, 3, 4, 5, 6}

Complementary Events

P(event) + P(not event) = 1
P(not event) = 1 − P(event)

Example: P(rain) = 0.35 → P(no rain) = 1 − 0.35 = 0.65

Experimental Probability

Based on actual results from trials.

P(event) = number of times event occurred ÷ total number of trials

Example: A coin is flipped 50 times and heads appears 23 times.
Experimental P(heads) = 23/50 = 0.46

Two-Step Experiments & Key Tips

Use a tree diagram or table to list all outcomes of combined experiments.

Example: Flipping a coin and rolling a die → 2 × 6 = 12 possible outcomes
P(heads and 6) = 1/12

Key Tips

• Probability can never be less than 0 or greater than 1
• Equally likely outcomes: P = favourable/total
• Check: all probabilities in a sample space must sum to 1
• For multi-step problems, multiply probabilities along branches of a tree diagram (for independent events)