Sheet № 186 · Foundation + Higher · AQA · Edexcel · OCR
Probability Scale and Basic Probability –
Basic probability is one of the first statistics topics you meet in GCSE Maths and is tested on every AQA, Edexcel and OCR Foundation and Higher paper. You need to understand the probability scale, calculate simple probabilities using equally likely outcomes, and use language like impossible, unlikely, even chance, likely and certain corr
§Key definitions
Probability
measures how likely an event is to happen. Every probability is a number from 0 to 1 inclusive.
Question:
A bag contains 4 red, 3 blue and 5 green counters. A counter is picked at random. Find the probability of picking (a) a red counter, (b) a counter that is not blue.
(a)
P(red) = 4/12 = 1/3.
(b)
P(blue) = 3/12 = 1/4. P(not blue) = 1 − 1/4 = 3/4.
Answer:
(a) 1/3, (b) 3/4.
§Formulas to memorise
P(event) = Number of favourable outcomes ÷ Total number of possible outcomes
P(not A) = 1 − P(A)
0 — Impossible (cannot happen). Example: rolling a 7 on a standard dice.
Between 0 and 0.5 — Unlikely. Example: rolling a 6 on a standard dice (probability 1/6).
0.5 — Even chance (equally likely to happen or not). Example: flipping heads on a fair coin.
Between 0.5 and 1 — Likely. Example: picking a red ball from a bag containing 8 red and 2 blue.
1 — Certain (must happen). Example: the sun rising tomorrow.
Probability: measures how likely an event is to happen. Every probability is a number from 0 to 1 inclusive.
Identify the total number of equally likely outcomes (the sample space).
Worked example
A bag contains 4 red, 3 blue and 5 green counters. A counter is picked at random. Find the probability of picking (a) a red counter, (b) a counter that is not blue.
Working:
⚠ Common mistakes
- ✗Probability outside 0 to 1. If your answer is negative or greater than 1, you have made an error.
- ✗Not simplifying fractions. Always reduce fractions to their simplest form.
- ✗Forgetting to count all outcomes. In words like MATHEMATICS, count every letter including repeats.
- ✗Confusing "at least one" with "exactly one." Read the question carefully to determine what is being asked.
✦ Exam tips
- →Probabilities can be written as fractions, decimals or percentages — choose whichever the question asks for, or use fractions by default.
- →When placing events on a probability scale, use the exact probability value (not just "unlikely" or "likely").
- →If all probabilities in a situation must add to 1 and you know all but one, subtract from 1 to find the missing probability.
- →For more advanced probability, see mutually exclusive events and expected frequency. For key formulas, visit our GCSE Maths formulas page.