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Probability Of God And Miracle

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Mathematics
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University of New Haven
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Question: Let 𝐺 = “God exists,” 𝑀 = “Miracles occur,” 𝑇 = 𝑃 → 𝑃, and 𝐷 = “Ducks exist.” Assume that Pr(𝐺 ) = 3⁄5 , Pr(𝑀) = 3⁄10 , Pr(𝐷) = 9⁄10 , and Pr(𝐺 |𝑀) = 9⁄10. Also assume that 𝐷 and 𝑀 are independent. Determine the following probabilities. Line Item A B C D Line Item E F G H G T T F F P T T F F M→G T T F T M T F T F P→P T T T T P T T F F M∧G T F F F M ∨G T T T F 𝐺 → (𝑀 ∨ 𝐺 ) T T T T a) Pr(¬𝑇) = 1 − Pr(𝑇) Pr(𝑇) = Pr(𝑃 → 𝑃 ) , According to the 1st truth table, 𝑃 → 𝑃 is a ? ...
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