Independent Events
One event does not affect the other.
Key idea
One event does not affect the other.
In depth
A and B are independent if P(A and B) = P(A)P(B), or equivalently, P(A | B) = P(A): one outcome does not affect the other. Independence is an assumption to be justified, not a given.
Worked example
Two coin flips: P(HH) = 1/2 × 1/2 = 1/4.
Formula
Real-world uses
- Checking that separate coin flips or independent machine failures do not affect each other
Common mistake
Assuming past outcomes influence future ones, as in gambler’s fallacy.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Independent Events?
One event does not affect the other. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Independent Events?
The key formula is P(A∩B) = P(A)P(B).
Where is Independent Events used in real life?
Real-world examples: Checking that separate coin flips or independent machine failures do not affect each other.
What should I learn before Independent Events?
Make sure you are comfortable with Conditional Probability, the previous topic in Probability & Statistics.
What is a common mistake with Independent Events?
Assuming past outcomes influence future ones, as in gambler’s fallacy.
How can I practise Independent Events?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Independent Events?
Move on to Multiplication Rule next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.