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

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

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Correct choice is (a) P(A|B) =

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) =

P(A∩B)

P(B)

.

Whereas formula’s P(A|B) =

P(A∩B)

P(A)

, P(A|B) =

P(A)

P(B)

, P(A|B) =

P(B)

P(A)

doesn’t satisfies the specified conditions.