(adsbygoogle = window.adsbygoogle || []).push({}); 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

P(A[1]) =.12

P(A[2])=.07

P(A[3])=.05

P(A[1] union A[2])=.13

P(A[1] union A[3])=.14

P(A[2] union A[3])=.10

P(A[1] intersects A[2] intersects A[3])=.01

1.what is the prob that the system does not have a type one defect?

2.what is the prob that the system has both type 1 and type 2 defects?

3. What is the prob that the system has both type 1 and type 2 defects but not a type 3 defect?

4.What is the prob that the system has at most two of these defects?

I know #1 is .88 and #4 is .99, but I am having difficulty understanding #2 and #3.

For #2: What is the probability that the system has both type 1 and type 2 defects, could that also include a system with ALL the defects (type 1, type 2, AND type 3 defects)? If so, I calculate the probability to be .07:

==>P(A int B) + P(A int B int C)

==>.12 + .07 - .13 + .01

==>.07

If so, then then the probability of #3 is .06.

Let me know if this is right or wrong.

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# Probability Syntax

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