Question
Download Solution PDFएक यादृच्छिक प्रयोग से जुड़ी A, B, C तीन परस्पर अपवर्जी और निष्कासी घटनाएँ हैं। यदि 3P(B) = 4P(A) और 3P(C) = 2P(B) है, तो P(A) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
A, B और C परस्पर अपवर्जी और निष्कासी घटनाएँ हैं:
⇒ P(A) + P(B) + P(C)= 1.....(i)
इसके अलावा
⇒ 3P(B) = 4P(A)
⇒ P(A) = \(\frac{3}{4} P(B)\)
और 3P(C) = 2P(B)
⇒ P(C) = \(\frac{2}{3}P(B)\)
(i) से
⇒ \(\frac{3}{4}P(B) +P(B)+ \frac{2}{3}P(B) =1\)
⇒ \(\frac{9P(B)+12P(B)+8P(B)}{12} = 1 \)
⇒ \(\frac{29P(B)}{12} =1\)
⇒ P(B) = \(\frac{12}{29}\)
⇒ P(A) = \(\frac{3}{4} \times \frac{12}{29} = \frac{9}{29}\)
∴ विकल्प (c) सही है।
Last updated on May 30, 2025
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