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

Question

A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) 0.14 P(A2)-0.09 P(A3) = 0.07 PlAi u Az) = 0.16 PA,U A3) = 0.17 PLA2 U A3)-0.13 P(A 1 n A2 n As) = 0.01 (a) What is the probability that the system does not have a type 1 defect? (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) What is the probability that the system has at most two of these defects?

Explanation / Answer

a) P(Does not have type 1 defect) = 1 - P(A) = 1 - 0.14 = 0.86

b) P(Both type I and type II defect) = P(A1) + P(A2) - P(A1 U A2) = 0.14 + 0.09 - 0.16 = 0.07

c) P(Both type I and Type II but not type II defect) = 0.07 - P(All three defects) = 0.07 - 0.01 = 0.06

d) P(At most two defects) = 1 - P(Three defects) = 1 - 0.01 = 0.99

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