Question
Download Solution PDFयदि , और , तो का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
दिया गया है,
\( P(A) = \frac{1}{3} \)
\( P(B) = \frac{1}{2} \)
\( P(A \cap B) = \frac{1}{4} \)
हमें \( P(A^C \cap B^C) \) की गणना करने की आवश्यकता है, जिसकी प्रायिकता न तो A और न ही B घटित होती है।
पूरक नियम का उपयोग करने पर:
\( P(A^C \cap B^C) = 1 - P(A \cup B) \)
अब, \(( P(A \cup B) \) ज्ञात करने के लिए समावेश-अपवर्जन सूत्र लागू करें:
\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)
दिए गए मानों को प्रतिस्थापित करने पर:
\( P(A \cup B) = \frac{1}{3} + \frac{1}{2} - \frac{1}{4} \)
सरल करने पर:
\( P(A \cup B) = \frac{4}{12} + \frac{6}{12} - \frac{3}{12} = \frac{7}{12} \)
अब, \(P(A^C \cap B^C) \) की गणना करने पर:
\( P(A^C \cap B^C) = 1 - \frac{7}{12} = \frac{5}{12} \)
इसलिए, सही उत्तर विकल्प 2 है।
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