Exercise · ZW-BAYES-THEOREM-006 · ★★☆ Intermediate

There are three cards: one red on both sides, one red and blue, one blue on both sides. A card is drawn at random and its visible face is red. What is the probability the other face is red?

Choose one option.

Show answer

A. 2/3

Explanation

\(\dfrac{\frac13\cdot1}{\frac13\cdot1+\frac13\cdot\frac12}=\dfrac23\). The double card has two red faces, the mixed one only one.

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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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