Sheet № 189 · Foundation + Higher · AQA · Edexcel · OCR
Mutually Exclusive Events –
Mutually exclusive events are a core probability concept tested on both Foundation and Higher GCSE Maths papers across AQA, Edexcel and OCR. Understanding when events cannot happen at the same time allows you to add probabilities — a rule that underpins many exam questions. You also need to know the complement rule and what exhaustive eve
§Key definitions
Question:
A bag contains 10 counters: 3 red, 4 blue and 3 green. A counter is picked at random. Find the probability of picking a red or green counter.
Answer:
The probability of picking a red or green counter is 3/5.
(a)
Walking and cycling are mutually exclusive. P(walks or cycles) = 0.35 + 0.15 = 0.50.
(b)
The three given modes are not exhaustive — some students go by car. Total of given = 0.35 + 0.25 + 0.15 = 0.75. P(car) = 1 − 0.75 = 0.25.
(c)
P(not B) = 1 − 0.35 = 0.65.
§Formulas to memorise
P(A or B) = P(A) + P(B) (for mutually exclusive events only)
P(not A) = 1 − P(A)
If they cannot (mutually exclusive), add the probabilities: P(A or B) = P(A) + P(B).
If you need the probability of something not happening, use P(not A) = 1 − P(A).
Worked example
A bag contains 10 counters: 3 red, 4 blue and 3 green. A counter is picked at random. Find the probability of picking a red or green counter.
Working:
⚠ Common mistakes
- ✗Adding probabilities for non-mutually-exclusive events. If events can happen at the same time (e.g. picking a red card and picking a king), you cannot simply add — you would double-count the overlap.
- ✗Probabilities not summing to 1. If a question gives all possible outcomes, check that your probabilities add to 1. If they do not, you have made an error.
- ✗Confusing "or" with "and." "Or" means either one (use addition for mutually exclusive). "And" means both together (use multiplication for independent — see the next topic).
✦ Exam tips
- →"Or" in probability usually means add (for mutually exclusive events).
- →If you are given all probabilities except one, subtract the total of the known probabilities from 1.
- →State clearly whether events are mutually exclusive to justify using the addition rule.
- →At Higher level, non-mutually-exclusive events need the formula P(A or B) = P(A) + P(B) − P(A and B) — but this is covered in Venn diagrams.
- →For combined events, see independent and dependent events. For key formulas, visit our GCSE Maths formulas page.