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 correctly. This guide covers all the essentials with worked examples and practice questions. For an overview of every topic, see our complete GCSE Maths topics list.

What Is Probability?

Probability measures how likely an event is to happen. Every probability is a number from 0 to 1 inclusive.

The Probability Scale

The probability scale runs from 0 to 1:

• 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.

Key Formulas

The first formula applies when all outcomes are equally likely. The second gives the probability of an event not happening.

Step-by-Step Method

1. Identify the total number of equally likely outcomes (the sample space).
2. Count how many outcomes satisfy the event you are interested in.
3. Divide: favourable outcomes ÷ total outcomes.
4. Simplify the fraction if possible.
5. Express as a fraction, decimal or percentage as required.

Worked Example 1 — Foundation Level

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.

Working:

Total counters = 4 + 3 + 5 = 12.

(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.

Worked Example 2 — Higher Level

Question: A letter is chosen at random from the word MATHEMATICS. Find the probability that the letter is (a) M, (b) a vowel, (c) not T.

Working:

Letters in MATHEMATICS: M, A, T, H, E, M, A, T, I, C, S — total 11 letters.

(a) M appears 2 times. P(M) = 2/11.

(b) Vowels (A, E, I): A appears 2 times, E once, I once = 4 vowels. P(vowel) = 4/11.

(c) T appears 2 times. P(T) = 2/11. P(not T) = 1 − 2/11 = 9/11.

Answer: (a) 2/11, (b) 4/11, (c) 9/11.

Worked Example 3 — Exam Style

Question: A fair spinner has sections numbered 1 to 8. Mark on a probability scale the probability of (a) spinning a 9, (b) spinning an even number, (c) spinning a number less than 7.

Working:

(a) P(9) = 0 — impossible. Mark at 0 on the scale.

(b) Even numbers: 2, 4, 6, 8 = 4 out of 8. P(even) = 4/8 = 0.5. Mark at 0.5 (even chance).

(c) Numbers less than 7: 1, 2, 3, 4, 5, 6 = 6 out of 8. P(<7) = 6/8 = 0.75. Mark at 0.75 (likely).

Answer: (a) 0 — impossible, (b) 0.5 — even chance, (c) 0.75 — likely.

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.

Practice Questions

Q1 (Foundation): A fair coin is flipped. What is the probability of getting tails?

Q2 (Foundation): A bag has 6 red and 4 yellow balls. What is the probability of picking a yellow ball?

Q3 (Higher): A card is drawn at random from a standard pack of 52 cards. Find the probability that the card is (a) a heart, (b) not a king.

Practise basic probability and the probability scale free on GCSEMathsAI.

Related Topics

• Expected Frequency
• Relative Frequency
• Mutually Exclusive Events

Summary

• Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).
• Calculate probability using P(event) = favourable outcomes ÷ total outcomes, when all outcomes are equally likely.
• Use P(not A) = 1 − P(A) for the complement of an event.
• Express probabilities as fractions, decimals or percentages, and always simplify fractions.
• The probability scale labels include impossible (0), unlikely, even chance (0.5), likely, and certain (1).