5. There are three types of batteries in a bin. Each battery has a different lifetime (in hours): Type 1's lifetime is exponential with rate 1=101. Type 2 has an exponential lifetime with rate 2=201, and Type 3 's uniform on [10,20]. Suppose that you choose a type ibattery from the bin with probability pifor i=1,2,3, with i=13pi=1. What is the probability that the battery you choose will last at least 15 hours? (Your answer may involve the pi's if necessary.)

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