Question
Download Solution PDFयदि
किन्हीं दो घटनाओं A और B के लिए
P(A ∪ B) = P(A ∩ B) है तो:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
P(A) + P(B) - P(A ∩ B) = P(A ∪ B)
गणना:
चूँकि; P(A ∪ B) = P(A ∩ B)
और, इस मान को सूत्र में रखने पर हमें प्राप्त होता है
⇒ P(A) - P(A ∩ B) + P(B) - P(A ∩ B) = 0 ----(1)
⇒ P(A) - P(A ∩ B) ≥ 0
⇒ P(B) - P(A ∩ B) ≥ 0
इसलिए, P(A) - P(A ∩ B) + P(B) - P(A ∩ B) ≥ 0 ----(2)
(1) और (2) से, हम प्राप्त करते हैं
⇒ P(A) - P(A ∩ B) = 0 और P(B) - P(A ∩ B) = 0
⇒ P(A) = P(A ∩ B) और P(B) = P(A ∩ B)
⇒ P(A) = P(B)
∴ संबंध P(A) = P(B) है।
Last updated on Jun 6, 2025
-> The HTET TGT Applciation Portal will reopen on 1st June 2025 and close on 5th June 2025.
-> HTET Exam Date is out. HTET TGT Exam will be conducted on 26th and 27th July 2025
-> Candidates with a bachelor's degree and B.Ed. or equivalent qualification can apply for this recruitment.
-> The validity duration of certificates pertaining to passing Haryana TET has been extended for a lifetime.
-> Enhance your exam preparation with the HTET Previous Year Papers.