Probability Basics — GCSE Mathematics Revision
Revise Probability Basics for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Experimental ProbabilityWhat 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 example
A bag contains 3 red, 5 blue and 2 green balls. Find P(blue). Total = 10. P(blue) = 5/10 = 1/2.
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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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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Probability Basics
Core concept
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. P…
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).