Question

Formula for Bayes theorem is ________

(a) P(A|B) = \(\frac{P(B│A)P(A)}{P(B)}\)

(b) P(A|B) = \(\frac{P(A)}{P(B)}\)

(c) P(A|B) = \(\frac{P(B│A)}{P(B)}\)

(d) P(A|B) = \(\frac{1}{P(B)}\)

The question was posed to me in an online quiz.

Query is from Bayes Theorem in portion Probability of Mathematics – Class 12

Answer 1

Correct answer is (a) P(A|B) = \(\frac{P(B│A)P(A)}{P(B)}\)

For explanation: Bayes theorem formula is P(A|B) = \(\frac{P(B│A)P(A)}{P(B)}\)

The formula provides relationship between P(A|B) and P(B|A). It is mainly derived from conditional probability formula P(A|B) and P(B|A). Where,

P(A|B) = \(\frac{P(A∩B)}{P(B)}\).

P(B|A) = \(\frac{P(B∩A)}{P(A)}\).