Before the distribution of certain statistical software, every forth compact dis

Question

Before the distribution of certain statistical software, every forth compact disk (CD) is tested for accuracy. The testing process consists of running four independent programs and checking the results. The failure rates for the four testing programs are, respectively, 0.02, 0.02, 0.03, and 0.03. (a) What is the probability that a CD was tested and failed any test? (b) Given that a CD was tested what is the probability that it failed program 3 or 4? (c) Given that a CD was defective, what is the probability that it was tested? (d) In a sample of 500, how many CDs would expect to be rejected?

Explanation / Answer

a) P(failed any test) = 1 - P(passing all tests)

= 1 - 0.98x0.98x0.97x0.97

= 1 - 0.9036

= 0.0964

b) P(failed program 3 or 4 given a CD was tested) = 1 - P(passed 3 and 4)

= 1 - 0.97x0.97

= 0.0591

c) P(tested | defective) = 1/4

d) P(passing all tests) = 0.9036

P(failing any test) = 1 - 0.9036 = 0.0964

Expected number of CDs to be rejected = 500x0.0964 = 48

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