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Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5 - Mathematics

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प्रश्न

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5

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उत्तर

P(A) = 0.4

P(A ∪ B) = 0.7

P(B/A) = 0.5

(i.e.,) `("P"("A" ∩ "B"))/("P"("A"))` = 0.5

(i.e.,) P(A ∩ B) = 0.5 × P(A)

= 0.5 × 0.4

= 0.2

Now P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ 0.7 = 0.4 + P(B) – 0.2

⇒ 0.7 = P(B) + 0.2

⇒ P(B) = 0.7 – 0.2 = 0.5

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पाठ 12: Introduction to probability theory - Exercise 12.3 [पृष्ठ २५९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 12 Introduction to probability theory
Exercise 12.3 | Q 10. (iv) | पृष्ठ २५९

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