Multiplication Rule
Probability of A and B.
Key idea
Probability of A and B.
In depth
P(A and B) = P(A)P(B | A). For independent events, P(B | A) = P(B). It lets you compute probabilities of sequences.
Worked example
Two cards without replacement: P(king then queen) = 4/52 × 4/51.
Formula
Real-world uses
- Calculating the chance that two independent components both work in an engineering system
Common mistake
Using the unconditional P(B) for dependent events.
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 Multiplication Rule?
Probability of A and B. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Multiplication Rule?
The key formula is P(A∩B) = P(A)P(B|A).
Where is Multiplication Rule used in real life?
Real-world examples: Calculating the chance that two independent components both work in an engineering system.
What should I learn before Multiplication Rule?
Make sure you are comfortable with Independent Events, the previous topic in Probability & Statistics.
What is a common mistake with Multiplication Rule?
Using the unconditional P(B) for dependent events.
How can I practise Multiplication Rule?
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 Multiplication Rule?
Move on to Law of Total Probability 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.