Question
Download Solution PDFदो घटनाओं A और B के लिए, P(A) = P(A|B) = 0.25 और P(B|A) = 0.5 है। निम्नलिखित में से कौन से सही हैं?
I. A और B स्वतंत्र हैं।
II. P(Ac ∪ Bc) = 0.875
III. P(Ac ∩ Bc) = 0.375
नीचे दिए गए कोड का उपयोग करके उत्तर चुनें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
\(P(A) = P(\frac{A}{B}) = 0.25\)
और \(P(\frac{B}{A}) = 0.5\)
I. \(P(\frac{B}{A}) = \frac{P(A∩ B)}{P(A)}\)
⇒ P(A∩B) = P(A) P(B|A)
⇒ P(A∩B) = 0.25 x 0.5 = 0.125
अब
⇒ \(P(B) = \frac{P(A∩ B)}{P(A|B)}\)
⇒ \(P(B) = \frac{0.125}{0.25} = 0.5\)
अब, P(A).P(B) = 0.25 x 0.5 = 0.125 = P(A∩B)
इस प्रकार A और B स्वतंत्र हैं
II. \(P(\overline A\cup \overline B ) = 1 – P(A ∩ B)\)
= 1 - 0.125 = 0.875
III. \(P(\overline A∩ \overline B ) = 1 – P(A \cup B)\)
= 1 - [P(A) + P(B) - P(A ∩ B)]
= 1 - [0.25 + 0.5 - 0.125]
= = 1 - 0.625 = 0.375
इसलिए सभी कथन I, II और III सही हैं।
∴ विकल्प (d) सही है।
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