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There are two strains of viruses. Virus (1 and virus Y. Virus Q is more deadly than virus Y. It has been known that the

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There are two strains of viruses. Virus (1 and virus Y. Virus Q is more deadly than virus Y. It has been known that the best way to differentiate the two viruses is their incubation time (the amount of time between when a person is infected and when they first show symptoms). Both viruses have exponentially distributed incubation times, but the mean incubation time for virus Q is 3 days, and 6 days for virus Y. (X'\"Exp(1/3) for people with virus Q, and X~Exp(1/6) for people with virus Y). Assume P(Q) = P(Y) = 1/2 since both viruses are equally prevalent. 1. Imagine a person visits a doctor exactly 1 day after they are infected and are already showing symptoms. What is the probability ofthis person having virus Q? (Hint: Find P(Q|X6|{X>3} n Y))

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