: 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.)?

Answer: 0.9862Step-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=0.64The proportion of Japanese chips are defective : P(D|J)=0.017The proportion of American chips are defective : P(D|U)=0.012Using 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 = 0.0138Then , the probability that a chip is defect-free=[tex]1-0.0138=0.9862[/tex]