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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Next step: Experimental Probability
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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.
Mini lesson for Probability Basics
1. Understand the core idea
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.
Can you explain Probability Basics without copying the notes?
2. Turn it into marks
A bag contains 3 red, 5 blue and 2 green balls. Find P(blue).
Underline the method, evidence, or command-word move that would earn credit in GCSE Probability.
3. Fix the likely mark leak
Watch for this mistake: Giving a probability greater than 1 or less than 0 — always check your answer is between 0 and 1.
Write one correction rule before doing another practice question.
Practise this topic
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Probability Basics practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Probability Basics is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Probability Basics question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Giving a probability greater than 1 or less than 0 — always check your answer is between 0 and 1." What should their next repair task be?
Answer: Do one Probability Basics question and review the mistake type.
Mark focus: Error correction and next-step practice.
Probability Basics flashcards
Core idea
What is the main idea in 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.
Common mistake
What mistake should you avoid in Probability Basics?
Giving a probability greater than 1 or less than 0 — always check your answer is between 0 and 1.
Practice
What is one useful practice task for Probability Basics?
Answer one Probability Basics question and review the mistake type.
Exam board
How should you use board notes for Probability Basics?
Use your own GCSE specification for exact paper wording and depth.
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
Exam-style questions for Probability Basics with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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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).