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Complement of an event

The complement of an event is the event that the original event does not happen.

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Student-friendly explanation

If the probability of an event is known, its complement helps us find the remaining chance. The two probabilities always add to 1. This is very useful when the direct counting is longer than counting the opposite case.

How to write this in exams

  1. 1

    Start with the exact idea

    The complement of an event is the event that the original event does not happen.

  2. 2

    Then show how to use it

    1. Identify the event. 2. Find or use its probability. 3. Subtract it from 1. 4. Write the complement clearly in words.

  3. 3

    Add one concrete example

    If the probability of getting a head on a fair coin is 1/2, then the probability of not getting a head is also 1/2.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 3/10 for no rain because the student repeats the given probability instead of subtracting it from 1.

Definition

The complement of an event is the event that the original event does not happen.

Example

If the probability of getting a head on a fair coin is 1/2, then the probability of not getting a head is also 1/2.

Rule to remember

P(not E) = 1 - P(E). The event and its complement together cover all possibilities.

Memory hook

Complement means the rest, so subtract from 1.

Examples and method

Worked example

If P(not getting a 6) on a die = 1 - 1/6 = 5/6. It is easier to count the single face 6 and subtract from 1.

Method to apply

1. Identify the event. 2. Find or use its probability. 3. Subtract it from 1. 4. Write the complement clearly in words.

Diagram support

A two-part bar or a Venn-style split can show the event and its complement adding to 1.

How CBSE asks it

Students are asked to find the probability of an event not happening, or to use 1 minus the given probability.

Avoid common mistakes

Common confusion

Students often subtract from the wrong number or confuse the complement with a completely different event.

Common wrong answer

A common wrong answer is 3/10 for no rain because the student repeats the given probability instead of subtracting it from 1.

Exam tip

Use complement when the opposite event is easier to count than the original event.

Quick check

If the probability of rain today is 3/10, what is the probability of no rain today?

The probability of no rain today is 1 - 3/10 = 7/10, because an event and its complement add up to 1.

Answer writing and exam use

1-mark answer

The complement of an event is the event that the original event does not happen.

2-mark answer

The complement of an event is the event that the original event does not happen. P(not E) = 1 - P(E). The event and its complement together cover all possibilities. If the probability of getting a head on a fair coin is 1/2, then the probability of not getting a head is also 1/2.

3-mark answer

If the probability of an event is known, its complement helps us find the remaining chance. The two probabilities always add to 1. This is very useful when the direct counting is longer than counting the opposite case. P(not E) = 1 - P(E). The event and its complement together cover all possibilities. If P(not getting a 6) on a die = 1 - 1/6 = 5/6. It is easier to count the single face 6 and subtract from 1. Students are asked to find the probability of an event not happening, or to use 1 minus the given probability. A common wrong answer is 3/10 for no rain because the student repeats the given probability instead of subtracting it from 1.
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