2. 01 points I Previous Answers DevoreStat9 2.E.048. My Notes Ask Your Teac ÷ A

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2. 01 points I Previous Answers DevoreStat9 2.E.048. My Notes Ask Your Teac ÷ A certain system can experience three different types of defects. Let A, (i1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) = 0.10 P(A2)-0.08 P(A3) = 0.06 p(A1 U A2) = 0.12 p(A1 UA3) = 0.13 P(A2 A30.12 AA0.01 (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.) 9000 (b) Given tha the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer tofour decimal places.) (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) 05 (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.) Need Help?Read It Talk to a Tutor Submit Answer Save Progress P Practice Another Version

Explanation / Answer

as P(A n B)=P(A)+P(B)-P(A U B)

P(A1 n A2)=0.1+0.08-0.12 =0.06

P(A2 n A3)=0.02

P(A1 n A3)=0.03

a)

P(A2|A1)=P(A1 n A2)/P(A1)=0.06/0.1=0.6

b)

P(A1 n A2 nA3)/P(A1) =0.01/0.1 =0.1

c)P(A1UA2uA3)=P(A1)+P(A2)+P(A3)-*P(A1nA2)-*P(A2nA3)-*P(A1nA3)+P(A1nA2nA3)=0.14

exaxctly one type defects =P(B)=P(A1)+P(A2)+P(A3)-2*P(A1nA2)-2*P(A2nA3)-2*P(A1nA3)+3*P(A1nA2nA3)=0.05

hene P(B|A1UA2uA3)=0.05/0.14

=0.3571

d)

P(A1 nA2 n A3c)/P(A1 n A2)=(0.06-0.01)/0.06=0.8333

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