Track 4 · Probability · Lesson 3 of 9
Conditional probability
Calculate conditional probabilities from two-way tables and from probabilities, and read the condition the right way round.
“Most people who default on a loan had a 60-month term” and “most 60-month loans default” sound alike but are completely different claims — in the lending data used here the first is false and the second is far from true. Conditional probability is the language that keeps such statements apart, and confusing them leads to wrong decisions in lending, medicine and courts.
A conditional probability — read “the probability of given ” — is the probability that happens when we already know that has happened.
Knowing shrinks the sample space: only outcomes inside are still possible. asks what fraction of that smaller world also belongs to .
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute P(A | B) from a two-way table by restricting to the condition's row or column
- Compute P(A | B) = P(A ∩ B)/P(B) from probabilities
- Translate everyday statements into the correct conditional probability
- Explain why P(A | B) and P(B | A) can be very different, with examples from lending and screening