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MathematicsEasyMCQTS EAMCET · 2010
मान लीजिए कि $A$ और $B$ दो ऐसी घटनाएँ हैं कि $P(A \cap B) = \frac{3}{25}$ और $P(B - A) = \frac{8}{25}$ है। तो,$P(B)$ का मान ज्ञात कीजिए।
A
$\frac{11}{25}$
B
$\frac{3}{11}$
C
$\frac{1}{11}$
D
$\frac{9}{11}$
Solution
(A) दिया गया है कि $P(A \cap B) = \frac{3}{25}$ और $P(B - A) = \frac{8}{25}$ है।
समुच्चय और प्रायिकता के गुणों के अनुसार,घटना $B$ को दो असंयुक्त समुच्चयों के संघ के रूप में व्यक्त किया जा सकता है: $(B - A)$ और $(A \cap B)$।
इसलिए,$P(B) = P(B - A) + P(A \cap B)$।
दिए गए मानों को प्रतिस्थापित करने पर:
$P(B) = \frac{8}{25} + \frac{3}{25} = \frac{11}{25}$।
समुच्चय और प्रायिकता के गुणों के अनुसार,घटना $B$ को दो असंयुक्त समुच्चयों के संघ के रूप में व्यक्त किया जा सकता है: $(B - A)$ और $(A \cap B)$।
इसलिए,$P(B) = P(B - A) + P(A \cap B)$।
दिए गए मानों को प्रतिस्थापित करने पर:
$P(B) = \frac{8}{25} + \frac{3}{25} = \frac{11}{25}$।
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