Exercise · ZW-BAYES-THEOREM-007 · ★★☆ Intermediate
A coin is fair or two-headed with equal probability. It is tossed three times and shows three heads. What is the probability it is the two-headed coin?
Choose one option.
Show answer
- B. 8/9
Explanation
\(\dfrac{\frac12}{\frac12+\frac12\cdot\frac18}=\dfrac89\). Each extra head makes the trick coin more credible.
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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