3. + 014 points Previous Answers DevoreStat9 2..048 My Notes Ask Your Teacher A

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3. + 014 points Previous Answers DevoreStat9 2..048 My Notes Ask Your Teacher 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 the following probabilities are true P(A1)-0.11 P(A2)-0.07 P(A3)-0.06 P(A1 U A2)0.1 PA1 U A3)0.14 P(A2 U A3)-0.11 RAI n A2 n A3)-0.01 (a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.) 06 (b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.) (c) Given that the system has at least one type of defect, what is the probablity that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.) 3571 Need Help?TaIk to a Tutor Submit Answer Save Progress Practice Another Version

Explanation / Answer

a) as P(A1 n A2)=P(A1)+P(A2)-P(A1 u A2)=0.11+0.07-0.12=0.06

hence P(type 2 defect|type 1 defect)=P(A2|A1)=0.06/0.11=0.5455

b)

P(A1 n A2 n A3|A1)=0.01/0.11 =0.0909

c)

P(exactly 2 defects|at least one defects)=0.05/0.14 =0.3571

d)

P(A1 nA2 nA3'|A1 nA2) =(P(A1 nA2)-P(A1nA2nA3))/P(A1 nA2) =(0.06-0.01)/0.06=0.8333

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