Conditional Probability
Probability of A given B.
Key idea
Probability of A given B.
In depth
P(A | B) = P(A and B)/P(B): the probability of A once we know B has occurred. Knowing B shrinks the sample space to B.
Worked example
Two dice sum to 8, given the first is 3: only (3, 5) works, so P = 1/6.
Formula
Real-world uses
- Estimating the chance a patient has a condition given a positive test
- Card game odds
Common mistake
Reversing the condition: P(A | B) ≠ P(B | A) generally.
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 Conditional Probability?
Probability of A given B. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Conditional Probability?
The key formula is P(A|B) = P(A∩B)/P(B).
Where is Conditional Probability used in real life?
Real-world examples: Estimating the chance a patient has a condition given a positive test; Card game odds.
What should I learn before Conditional Probability?
Make sure you are comfortable with Mutually Exclusive Events, the previous topic in Probability & Statistics.
What is a common mistake with Conditional Probability?
Reversing the condition: P(A | B) ≠ P(B | A) generally.
How can I practise Conditional Probability?
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 Conditional Probability?
Move on to Independent Events 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.