A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = 32 P(A) and P(C) = 12 P(B). - Mathematics and Statistics

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Sum

A, B, and C are mutually exclusive and exhaustive events associated with the random experiment. Find P(A), given that P(B) = `3/2` P(A) and P(C) = `1/2` P(B).

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Solution

P(B) = `3/2` P(A) and P(C) = `1/2` P(B)

Since A, B, C are mutually exclusive and exhaustive events,
∴ P(A ∪ B ∪ C) = P(A) + P(B) + P(C) = 1

∴ `"P"("A") + 3/2"P"("A") + 1/2"P"("B")` = 1

∴ `"P"("A") + 3/2"P"("A") + 1/2 xx 3/2"P"("A")` = 1

∴ `"P"("A") + 3/2"P"("A") + 3/4"P"("A")` = 1

∴ `"P"("A") xx (1 + 3/2 + 3/4)` = 1

∴ `"P"("A") xx (13/4)` = 1

∴ P(A) = `4/13`

Concept: Addition Theorem of Probability
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Chapter 7: Probability - Miscellaneous Exercise 7 [Page 110]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 7 Probability
Miscellaneous Exercise 7 | Q 6 | Page 110

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