A certain system can experience three different types of defects. Let A_i(i = 1,

Question

A certain system can experience three different types of defects. Let A_i(i = 1, 2, 3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A_1) = 0.15 P(A_2) = 0.09 P(A_3) = 0.07 P(A_1 A_2) = 0.17 P(A_1 A_3) = 0.18 P(A_2 A_3) = 0.14 P(A_1 A_2 A_3) = 0.01 What is the probability that the system does not have a type 1 defect? What is the probability that the system has at most two of these defects? What is the probability that the system has both type 1 and type 2? What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?

Explanation / Answer

The probability that a system does not have a type 1 defect is:

1-0.15=0.85

The probability that the sytem has both type 1 and type 2 defects is:

0.15*0.09=0.0135

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