Exercise · ZW-BAYES-THEOREM-004 · ★★☆ Intermediate
Urn A has 3 red and 2 blue balls; urn B has 1 red and 4 blue. A fair coin picks an urn and a red ball comes out. What is the probability it came from A?
Choose one option.
Show answer
- C. 3/4
Explanation
\(\dfrac{\frac12\cdot\frac35}{\frac25}=\dfrac34\). The 3/5 ignores that B can also give red.
Review the concept: Bayes' theorem
Bayes' theorem inverts a conditional probability: it gives the probability \(P(B_j\mid A)\) of a cause \(B_j\) given an observed effect \(A\), from the probability of the effect given that cause.
\[P(B_j\mid A)=\frac{P(A\mid B_j)\,P(B_j)}{\sum_{i}P(A\mid B_i)\,P(B_i)}\]
More practice problems: bayes' theorem
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