What is the probability that a tablet computer will fail catastrophically?

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When a tablet computer develops a problem, it is either due to the software or due to the hardware. In the past, software has been the problem 65% of the time. The probability that the tablet fails catastrophically given that there is a software problem is 0.1 while the probability that it fails catastrophically given that there is a hardware problem is 0.25.

(a) What is the probability that a tablet computer will fail catastrophically?

(b) Given that a tablet computer has failed catastrophically, what is the probability that the problem is software related?

(c) When a tablet fails catastrophically, customers call a technical support helpline. Based on your calculations in part (b), would you recommend that the technician check the tablet hardware or the software first?

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