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

Category: QuestionsFormula for conditional probability P(A|B) is _______
Editor">Editor Staff asked 11 months ago

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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1 Answers
Editor">Editor Staff answered 11 months ago

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.