Question

Formula for conditional probability P(A|B) is _______

(a) P(A|B) = \(\frac{P(A∩B)}{P(B)}\)

(b) P(A|B) = \(\frac{P(A∩B)}{P(A)}\)

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

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

This question was posed to me in quiz.

My question is based upon Bayes Theorem in chapter Probability of Mathematics – Class 12

Answer 1

Correct choice is (a) P(A|B) = \(\frac{P(A∩B)}{P(B)}\)

For explanation I would say: Conditional probability P(A | B) indicates the probability of event ‘A’ happening given that event B has happened.

Which in formula can be written as P(A|B) = \(\frac{P(A∩B)}{P(B)}\).

Whereas formula’s P(A|B) = \(\frac{P(A∩B)}{P(A)}\), P(A|B) = \(\frac{P(A)}{P(B)}\), P(A|B) = \(\frac{P(B)}{P(A)}\) doesn’t satisfies the specified conditions.