Exercise · ZW-BAYES-THEOREM-003 · ★☆☆ Basic
Which is the correct statement of Bayes' theorem?
Choose one option.
Show answer
- D. \(P(B\mid A)=\dfrac{P(A\mid B)\,P(B)}{P(A)}\)
Explanation
It comes from writing \(P(A\cap B)\) in two ways: \(P(B\mid A)P(A)=P(A\mid B)P(B)\), then solving.
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
- ZW-BAYES-THEOREM-001 If P(B)=0.3, P(A| B)=0.8 and P(A)=0.4, what is P(B| A)?
- ZW-BAYES-THEOREM-002 A coin is either fair or two-headed, with equal probability. It is tossed once and shows heads. Wha…
- ZW-BAYES-THEOREM-004 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 ba…
- ZW-BAYES-THEOREM-005 Three machines make 50 %, 30 % and 20 % of the parts, with 1 %, 2 % and 5 % defective. A part is fo…
- ZW-BAYES-THEOREM-006 There are three cards: one red on both sides, one red and blue, one blue on both sides. A card is d…
- ZW-BAYES-THEOREM-007 A coin is fair or two-headed with equal probability. It is tossed three times and shows three heads…
- ZW-BAYES-THEOREM-008 A disease affects 1 %. The test is positive for 99 % of the sick and 5 % of the healthy. If you tes…
- ZW-BAYES-THEOREM-009 If 0<P(B)<1 and P(A| B)=P(A| B^c)>0, what follows for P(B| A)?