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Question
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).
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`
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