Question
Download Solution PDFIf an event B has occurred and has P(B) = 1, the conditional probability P(A|B) is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation
If the event B occurs does not change the probability that event A occurs, and event A and B are the independent event then
⇒ P(A I B) = P(A)
According to bayes’s theorem It states the relation between the probabilities of A and B, P(A) and P(B) and the conditional probabilities of A gives B and B gives A.
⇒ P(A I B) and P(B I A)
⇒ P(A I B) = P(B I A).P(A)/P(B)
⇒ P(B I A) = P(A ∩ B)/P(A)
⇒ P(A ∩ B) = P(A).P(B)
⇒ P(A I B) = P(A ∩ B).P(A)/P(A). P(B)
⇒ P(A I B) = P(A). P(B).P(A)/P(A).P(B)
⇒ P(A I B) = P(A)
∴ The value of P(A I B) is P(A)Last updated on Jun 13, 2025
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