Question
Download Solution PDFयदि A और B दो घटनाएं इस प्रकार हैं जिससे \(\rm P(A')=\frac13, P(B')=\frac23\) और \(\rm P(A\cap B)=\frac15\) है, तो \(\rm P(\frac{\bar A}{B})\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
माना कि दो घटनाएं A और B है
\(\rm P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}\)
\(\rm P(A)=1-P(A')\)
\(\rm P(A'\cap B)=P(B)-P(A\cap B)\)
गणना:
यहाँ, \(\rm P(A')=\frac13, P(B')=\frac23\) और \(\rm P(A\cap B)=\frac15\)
\(\rm P(B)=1-P(B')=1-\frac23=\frac13\) (∵ \(\rm P(A)=1-P(A')\))
\(\rm P(\frac{\bar A}{B})=\frac{P(\bar A\cap B)}{P(B)}\) (∵ \(\rm P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}\))
\(\rm =\frac{P(B)-P(A\cap B)}{P(B)}\) (∵ \(\rm P(A'\cap B)=P(B)-P(A\cap B)\))
\(=\rm \frac{\frac13-\frac15}{\frac13}\)
\(=\rm {\frac{2}{15}}\times3\)
\(=\rm {\frac{2}{5}}\)
अतः विकल्प (2) सही है।
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