Question
Download Solution PDFयदि P(A) = 0.4, P(B) = 0.8 और P(B|A) = 0.6 तो P(A ∪ B) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
दो घटनाओं A और B के लिए:
- P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- B दी गई A की सप्रतिबन्ध प्रायिकता को इस प्रकार परिभाषित किया गया है: P(B|A) = \(\rm \dfrac{P(A\cap B)}{P(A)}\) , जब P(A)> 0
गणना:
P(B|A) = \(\rm \dfrac{P(A\cap B)}{P(A)}\) हम प्राप्त करते हैं:
0.6 = \(\rm \dfrac{P(A\cap B)}{0.4}\)
⇒ P(A ∩ B) = 0.24
अब P(A ∪ B) = P(A) + P(B) - P(A ∩ B) के संबंध का उपयोग करते हुए, हम पाते हैं:
P(A ∪ B) = 0.4 + 0.8 - 0.24 = 0.96
Last updated on Jun 20, 2025
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