Events and their Complements
An event is a selected part of the sample space, and its complement is the event that it does not happen.
Practice This ConceptMain explanation
Teacher explanation
If E is an event, then not E includes all outcomes outside E. Since an event and its complement together cover the full sample space, their probabilities add to 1.
Example
For a die, if E is getting an even number, then not E is getting an odd number.
Simple analogy
Complement means everything outside the event, not just the opposite word that first comes to mind.
Common confusion
Students sometimes think the complement of greater than 4 is less than 4, forgetting the outcome equal to 4.
Exam tip
When finding a complement, include every outcome that does not satisfy the event, including boundary values.
Study the events and their complements diagram carefully
Use the labelled diagram to keep events and their complements clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of events and their complements in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on events and their complements.
Revision cue
Revise events and their complements through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of events and their complements in one clean line.
2-mark use
Define events and their complements and add one example or condition.
3-mark use
Explain events and their complements, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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