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Conditional Probability
P(A|B) restricts the sample space to outcomes in B, then measures the part also in A.
How it works
P(A|B) restricts the sample space to outcomes in B, then measures the part also in A. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
Of 10 music students, 4 study art. Find P(art|music).
- Restrict the denominator to the 10 music students.
- Four meet both conditions.
- Simplify 4/10.
P(art|music)=2/5.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Explain when P(A|B)=P(A) indicates independence.
Questions learners ask
What is the key idea in conditional probability?
P(A|B) restricts the sample space to outcomes in B, then measures the part also in A.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.