Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Introduction to Complementary Events
Unlock Audio Lesson
Today, we’re going to talk about complementary events. Can someone explain what we mean by complementary events in probability?
I think it’s about events that cannot happen at the same time.
That’s correct! Complementary events are those that cover all possible outcomes for an experiment. For example, if an event E occurs, then 'not E' cannot happen at the same time. Let’s say flipping a coin where E is 'getting heads' — what is 'not E'?
Getting tails!
Exactly! Now, remember this memory aid: 'When E takes the floor, not E shuts the door.' It reminds us that if an event occurs, its complement does not!
Mathematics of Complementary Events
Unlock Audio Lesson
Now, moving on to the mathematics — if P(E) is the probability of an event happening, how do we express P(not E)?
Isn’t it like taking 1 minus P(E)?
Yes! The formula is P(not E) = 1 - P(E). Can anyone provide an example using this formula?
If P(E) is 0.65, the probability of not E would be 1 - 0.65, which equals 0.35.
Perfect! So it's crucial to use this equation to understand how events and their complements interrelate.
Practical Applications of Complementary Events
Unlock Audio Lesson
Let’s think about a real-world application. Suppose we know the probability of it raining today is 0.65. What would be the probability that it won’t rain?
So we just do 1 - 0.65 again, which gives us 0.35!
That’s right! Understanding complementary events helps us make better predictions based on probabilities. Why do you think they are important in decision-making?
They help us evaluate risks better!
Exactly! Remember, knowing the probability of an event also tells us the likelihood of it not happening, which is crucial in planning!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In probability theory, complementary events are those events that are mutually exclusive, where one event occurs if and only if the other does not. The probability of not occurring an event can be calculated through the formula P(not E) = 1 - P(E), emphasizing the relationship between the probability of an event and its complement.
Detailed
Complementary Events
In this section, we explore complementary events in probability theory. Complementary events are a fundamental concept where the occurrence of one event implies that the other event does not occur. Mathematically, if P(E) represents the probability of an event E occurring, then P(not E) — the probability of E not occurring — is given by the equation:
%20%3D%201%20-%20P(E)
For example, if the probability of raining today is given as 0.65, we can easily determine that the probability of it not raining is:
P(not raining) = 1 - 0.65 = 0.35.
This highlights how complementary events work in terms of total probability summing to 1, which is a crucial principle in probability theory.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Understanding Complementary Events
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
If P(E) is the probability of an event E, then the probability of the event not happening is:
P(not E) = 1 - P(E)
Detailed Explanation
Complementary events are two outcomes that cannot occur at the same time. If we know the probability of an event happening (P(E)), we can find the probability of it not happening (P(not E)) by subtracting P(E) from 1. This is because the total probability of all possible outcomes must equal 1. Thus, if something happens with a probability P(E), then its complement, which is not happening, will have a probability equal to 1 minus P(E).
Examples & Analogies
Think of flipping a coin. If the probability of getting heads (P(heads)) is 0.5, then the probability of not getting heads (which means getting tails, or P(not heads)) is also 0.5. So, if you were to flip the coin, there's just as much chance you will see tails as you will see heads.
Example of Complementary Events
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
The probability of it raining today is 0.65. What is the probability that it will not rain?
Solution:
P(not raining) = 1 - 0.65 = 0.35
Detailed Explanation
In this example, the probability of rain today has been given as 0.65. To find the probability of it not raining, we use the complementary event formula. We subtract the probability of it raining from 1, so we calculate 1 - 0.65, which results in 0.35. This means there is a 35% chance that it will not rain today.
Examples & Analogies
Imagine you are planning a picnic and hear that there is a 65% chance of rain. To figure out how likely it is that the weather will be clear and perfect for your picnic, you can think of this as a complementary event. If there is a 65% likelihood of rain, then there is a 35% chance that it will be sunny. This gives you a clearer idea of the risk versus reward when deciding to go ahead with your picnic plans.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Complementary Events: Two events that are mutually exclusive; one event happening means the other does not.
-
P(E): The probability that event E occurs.
-
P(not E): The probability that event E does not occur, calculated as 1 - P(E).
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
If the probability of it raining today is 0.65, the probability that it will not rain is 0.35.
-
If the probability of flipping a heads on a coin is 0.5, the probability of not flipping heads (flipping tails) is also 0.5.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
If E is high, then not E's shy; together, they make 1, oh my!
📖 Fascinating Stories
-
Imagine a party planning where friends can only attend or miss; if one friend shows, the others are out of luck — that's the essence of complementary events!
🧠 Other Memory Gems
-
E = Event, not E = No Event; Together they complete the entire probability spectrum.
🎯 Super Acronyms
C.E. = Complementary Events = One happens, the other is absent!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Complementary Events
Definition:
Two events are complementary if the occurrence of one event means the other cannot occur.
-
Term: Probability
Definition:
A measure of how likely an event is to occur, ranging from 0 to 1.
-
Term: Event E
Definition:
A specific outcome or result of a probability experiment.
-
Term: P(E)
Definition:
The probability that event E occurs.
-
Term: P(not E)
Definition:
The probability that event E does not occur (complement of E).