Question
Download Solution PDFयदि कोई घटना B घटित हुई है और P(B) = 1 है, तो सशर्त प्रायिकता P(A|B) बराबर है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या
यदि घटना B घटित होने से घटना A के घटित होने की प्रायिकता नहीं बदलती है, और घटना A और B स्वतंत्र घटना हैं तो
⇒ P(A I B) = P(A)
बेयस के प्रमेय के अनुसार यह A और B, P(A) और P(B) की संभावनाओं के बीच संबंध बताता है और A की सशर्त प्रयिकताएँ B और B, A देता है।
⇒ P(A I B) और 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)
∴ P(A I B) का मान P(A) है।Last updated on Jul 8, 2025
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