Independent and Dependent Events
Independent events don't affect each other.
About this topic
Two events are independent if one does not change the probability of the other, such as two coin flips; then P(A and B) = P(A) × P(B). Events are dependent if the outcome of the first alters the second, such as drawing cards without replacement; then P(A and B) = P(A) × P(B given A).
To test for independence, check whether P(B given A) equals P(B). Example: the probability of two heads in a row is 1/2 × 1/2 = 1/4. Drawing two aces from a deck without replacement has probability 4/52 × 3/51 = 1/221, about 0.45%, much lower than with replacement, which is 1/169. The word replacement is the clue: putting the item back keeps events independent.
Independence is used when assessing system reliability: if a device has three independent parts that each work 90% of the time and all must work, then it functions with probability 0.9³ = 0.729. Dependent events appear in weather, where a rainy morning raises the chance of a rainy afternoon.
Common misconceptions are that independent is the same as mutually exclusive, which it is not; exclusive events with nonzero probabilities are actually dependent, since one occurring rules out the other.
Key ideas
- Independent: P(A and B) = P(A)P(B)
- Drawing without replacement is dependent
- Coin flips are independent
Quick check
Use cases: where Independent and Dependent Events helps
- Homework: review the key idea behind Independent and Dependent Events before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Independent and Dependent Events without notes.
- Visual learning: play with the interactive lab to see how Independent and Dependent Events changes when you adjust its inputs.
- Teaching a friend: explain Independent and Dependent Events in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Independent and Dependent Events?
Independent events don't affect each other.
What will I learn in Independent and Dependent Events?
Independent: P(A and B) = P(A)P(B). Drawing without replacement is dependent. Coin flips are independent.
Is Independent and Dependent Events part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Independent and Dependent Events lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Independent and Dependent Events?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.