Module 2 · Probability Foundations · Topic 6
Conditional Probability. P(A | B) is the probability of A occurring given that B has already occurred. It “restricts” the sample space to only those outcomes where B happened.
P(A | B) = P(A ∩ B) / P(B), where P(B) > 0
P(A | B) = P(A and B) / P(B) — Probability of A after restricting attention to cases where B occurred.P(A | B) = P(B | A)P(A) / P(B) — Updates a prior probability after observing evidence.In a class, 60% study math, 40% study science, and 20% study both. P(math | science) = P(math ∩ science) / P(science) = 0.20 / 0.40 = 0.50.
Read P(A | B) as “the probability of A given B.” The event after the vertical bar is the condition - what you already know happened.
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