LEC13 Discrete Dist & Conditioning

LEC13 Discrete Dist & Conditioning - Use the Law of...

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Use the Law of Total Probability to Solve Problems A company orders boxes of 10 machined parts from two suppliers. Supplier 1 supplies 70 percent and has defective rate .03. Supplier 2 supplies 30 percent and has defective rate .05. Find the probability of 0 defectives in a box. Find the probability of 1 defective in a box Find the expected number of defectives in a box
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r.v. S = supplier: P(S=1) = .7 P(S=2) = .3 r.v. X = number of defectives in box of 10 given S=1, P(X=0) = 10 0 03 97 737 0 10 = . . . given S=2, P(X=0) = 10 0 05 95 599 0 10 = . . . ( 29 ( 29 P X P X S P S P X S P S ( ) ( / ) ( ) ( / ) ( . . . . . . . = = = = = + = = = = + = 0 0 1 1 0 2 2 10 0 03 97 7 10 0 05 95 3 696 0 10 0 10 ( 29 ( 29 P X P X S P S P X S P S ( ) ( / ) ( ) ( / ) ( . . . . . . . = = = = = + = = = = + = 1 1 1 1 1 2 2 10 1 03 97 7 10 1 05 95 3 255 1 9 1 9 2
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Storm Damage The number of storms that occur in a ten year period has the Poisson distribution with mean 0.4. If a storm does occur, the probability of bridge damage is 0.05. Find the probability no bridge damage
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LEC13 Discrete Dist & Conditioning - Use the Law of...

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