Question

A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote...

A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i.

Suppose that P(A1) = 0.25, P(A2) = 0.29, P(A3) = 0.33, P(A1 ∪ A2) = 0.5, P(A1 ∪ A3) = 0.53, P(A2 ∪ A3) = 0.54, P(A1 ∩ A2 ∩ A3) = 0.02

(a) Find the probability that the system has exactly 2 of the 3 types of defects.

(b) Find the probability that the system has a type 1 defect given that it does not have a type 2 or type 3 defect.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(a)

The probability that system have defects A1 and A2 but not A3 is

The probability that system have defects A1 and A3 but not A2 is

The probability that system have defects A2 and A3 but not A1 is

The probability that the system has exactly 2 of the 3 types of defects

(b)

The probability that system does not defect 2 or 3:

And

The probability that the system has a type 1 defect given that it does not have a type 2 or type 3 defect is

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