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465.One Bulb Against Ten

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classical probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Ten independent light bulbs have lifetimes TiExp(1/10)T_i \sim \mathrm{Exp}(1/10) (mean 10), and an eleventh bulb has lifetime XExp(1/90)X \sim \mathrm{Exp}(1/90) (mean 90). Find P[X>T1++T10]P[X > T_1 + \cdots + T_{10}].

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