GCSE Mathematics Revision — Probability Basics
Revise Probability Basics for GCSE Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Probability Basics?
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). The probability of an event = number of favourable outcomes ÷ total number of possible outcomes. Probabilities of all possible outcomes sum to 1. You need to understand mutually exclusive events (P(A or B) = P(A) + P(B)) and independent events (P(A and B) = P(A) × P(B)).
Step-by-step explanationWorked examples
Worked example
A bag contains 3 red, 5 blue and 2 green balls. Find P(blue). Total = 10. P(blue) = 5/10 = 1/2.
Practise this topic
Start with low-focus cards for Probability Basics, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Giving a probability greater than 1 or less than 0 — always check your answer is between 0 and 1.
- 2Adding probabilities for independent events instead of multiplying (AND = multiply, OR = add for mutually exclusive).
- 3Not listing all outcomes in the sample space — missing outcomes skews the probability.
- 4Confusing theoretical probability with experimental (relative frequency) probability.
Probability Basics exam questions
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Frequently asked questions
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated from equally likely outcomes. Experimental probability (relative frequency) is calculated from actual trials. As the number of trials increases, experimental probability approaches theoretical probability.
When do I add vs multiply probabilities?
Add probabilities for mutually exclusive events (OR). Multiply probabilities for independent events (AND). If events are not mutually exclusive, use P(A or B) = P(A) + P(B) - P(A and B).