Mutually Exclusive Events
Mutually exclusive events are outcomes that cannot both happen on the same trial, so one outcome happening automatically rules out the other, such as rolling a 3 and rolling a 5 on the same dice roll. For mutually exclusive events, the probability that one OR the other happens is found by adding their individual probabilities, and this addition rule is tested throughout the Probability strand of GCSE Statistics.
Before you start
Make sure you're comfortable with these topics first:
Method
- Decide whether the two events can happen at the same time; if they cannot, they are mutually exclusive.
- For mutually exclusive events, find P(A or B) by adding P(A) and P(B).
- Remember that the probabilities of all mutually exclusive outcomes of an experiment must add up to 1.
- Use this fact to find a missing probability by subtracting the known probabilities from 1.
- Check whether events can happen together; if they can, the simple addition rule cannot be used without adjustment.
- Double-check by adding all the probabilities in the question to make sure the total is sensible.
Worked example
A spinner lands on red, blue, green or yellow. P(red) = 0.25, P(blue) = 0.3, P(green) = 0.2. Find P(yellow), and find P(red or green).
- All four outcomes are mutually exclusive and cover every possibility, so their probabilities sum to 1.
- P(red) + P(blue) + P(green) = 0.25 + 0.3 + 0.2 = 0.75.
- P(yellow) = 1 - 0.75 = 0.25.
- Red and green cannot both occur on the same spin, so P(red or green) = P(red) + P(green).
- P(red or green) = 0.25 + 0.2 = 0.45.
- Final answer: P(yellow) = 0.25; P(red or green) = 0.45.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1P(A) = 0.4 and P(B) = 0.35, where A and B are mutually exclusive. Find P(A or B).Show answer
Answer: 0.75 (0.4 + 0.35)
Q2A bag has only red, blue and green counters. P(red) = 0.5 and P(blue) = 0.2. Find P(green).Show answer
Answer: 0.3 (1 - 0.5 - 0.2)
Q3Are 'rolling an even number' and 'rolling a 5' on a normal six-sided dice mutually exclusive?Show answer
Answer: Yes (5 is odd, so there is no overlap)
Q4P(rain) = 0.3 and P(snow) = 0.05 on a given day, and rain and snow are mutually exclusive that day. Find P(rain or snow).Show answer
Answer: 0.35 (0.3 + 0.05)
Q5A card is drawn at random from a normal 52-card pack. Find P(drawing a King or a Queen).Show answer
Answer: 2/13 (8/52, since 4 kings and 4 queens are mutually exclusive)
Q6A game has four mutually exclusive outcomes: win, draw, lose, abandoned. P(win) = 0.45, P(draw) = 0.2, P(abandoned) = 0.05. Find P(lose).Show answer
Answer: 0.3 (1 - 0.45 - 0.2 - 0.05)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A biased dice can only show a 1, 2 or 3. P(1) = 0.2 and P(2) = 0.45. Work out P(3).
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A charity raffle gives every ticket exactly one prize: a hamper, a voucher or a toy, so the events are mutually exclusive. P(hamper) = 0.15 and P(voucher) = 0.4. (a) Work out P(toy). (b) Work out P(hamper or toy).
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A bag contains only red, blue, green and white beads. A bead is picked at random. P(red) = 0.3 and P(white) = 0.1. P(blue) = 2 x P(green). Given that red, blue, green and white are mutually exclusive and cover all the beads, work out P(green) and P(blue).
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the mutually exclusive events worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 17 of GCSE Statistics Foundation Workbook 2 and chapter 23 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
Other cuts of this worksheet:
Next topics
Not quite what you needed?
Tell us what is missing on mutually exclusive events, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.