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: A personal computer manufacturer buys 36% of its chips from Japan and the rest from the United St...
A personal computer manufacturer buys 36% of its chips from Japan and the rest from the United States. Of the Japanese chips, 1.7% are defective, and 1.2% of the American chips are defective.

Find the probability that a chip is defect-free. (Round your answer to four decimal places.)?

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JeanaShupp

Answer: 0.9862

Step-by-step explanation:

Given : The probability that the chips belongs to Japan: P(J)= 0.36

The probability that the chips belongs to United States : P(U)= 1-0.36=0.64

The proportion of Japanese chips are defective : P(D|J)=0.017

The proportion of American chips are defective : P(D|U)=0.012

Using law of total probability , we have

[tex]P(D)=P(D|J)\times P(J)+P(D|U)\times P(U)\\\\\Rightarrow\ P(D)=0.017\times0.36+0.012\times0.64=0.0138[/tex]

Thus , the probability that chip is defective = 0.0138

Then , the probability that a chip is defect-free=[tex]1-0.0138=0.9862[/tex]

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