COMPLEMENT OF AN EVENT

Complement Of An Event

Definition Of Complement Of An Event

The Complement of an Event is all the other possible outcomes of the respective experiment.

If A is an event of an experiment, then its complement is denoted by A^c.

Video Examples: Complement of an Event - Probability

Example of Complement of an Event

Suppose a fair six-sided die is rolled.
Let A be the event of rolling a 3. Then, the complement of
A = A^c = {1, 2, 4, 5, 6}.

Solved Example onComplement of an Event

Ques: John has 10 cards, numbered from 1 through 10, out of which he chooses one card randomly. Find the probability of John not choosing a card numbered 7.

Choices:

A.1/10
B.7/10
C.3/10
D.9/10
Correct Answer: D

Solution:

Step 1: The probability of John choosing the card numbered 7 is 1/10.
Step 2: The probability of the complement of this event is 1 - 1/10 = 9/10 .

Quick Summary

The complement of an event includes all outcomes not in the event.
The probability of an event and its complement always add up to 1.

\[ P(A^c) = 1 - P(A) \]

🍎 Teacher Insights

Use real-world examples, like rolling a die or drawing cards, to illustrate the concept of complements. Emphasize that the complement includes *everything* that is *not* the event.

🎓 Prerequisites

Basic set theory
Understanding of probability
Sample space

Check Your Knowledge

Q1: A coin is flipped. If the event A is getting heads, what is the complement of A?

Getting tails Getting heads Not flipping the coin Flipping two coins

Q2: If the probability of event B is 0.3, what is the probability of the complement of B?

0.3 0.7 0 1

Frequently Asked Questions

Q: What is the relationship between an event and its complement?
A: An event and its complement are mutually exclusive and exhaustive; together, they cover the entire sample space.

Q: How do you calculate the probability of the complement of an event?
A: Subtract the probability of the event from 1: P(A^c) = 1 - P(A).