Question
Download Solution PDFयदि A और B ऐसे दो अनुवृत्त (इवेंट) हैं कि P(A नहीं) = \(\rm \frac{7}{10}\), P(B नहीं) = \(\rm \frac{3}{10}\) और P(A|B) = \(\rm \frac{3}{14}\) है, तो P(B|A) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
P(A नहीं) = \(\rm \frac{7}{10}\), और P(B नहीं) = \(\rm \frac{3}{10}\)
P(A|B) = \(\rm \frac{3}{14}\)
प्रयुक्त सूत्र:
- \(\rm P(B|A) = \frac{P(A\cap B)}{P(A)}\)
- \(\rm P(A|B) = \frac{P(A\cap B)}{P(B)}\)
- P(A) = 1 - P(A नहीं)
- P(B) = 1 - P(B नहीं)
गणना:
हमारे पास है
\(\rm P(\bar{B}) = 0.3, P(\bar{A}) = 0.7\)
⇒ P(B) = 1 - 0.3 = 0.7 और
P(A) = 1 - 0.7 = 0.3
⇒ P(A) = 0.3 ----(1)
हम जानते हैं कि,
\(\rm P(A|B) = \frac{P(A\cap B)}{P(B)}\)
⇒ \(\frac{3}{14} \) = \(\frac{P(A\cap B)}{0.7}\) (∵ P(A|B) = \(\rm \frac{3}{14}\))
⇒ \(\rm P(A\cap B)\) = 0.15 ----(2)
हम जानते हैं कि,
\(\rm P(B|A) = \frac{P(A\cap B)}{P(A)}\)
⇒ P(B|A) = \(\rm \frac{0.15}{0.3}\) [समीकरण (1) और (2) से]
⇒ P(B|A) = 0.5 = \(\rm \frac{1}{2}\)
∴ P(B|A), \(\rm \frac{1}{2}\) के बराबर है
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