A personal computer manufacturer buys 36% of its chips from Japan and the rest from the United States. Of the Japanese chips, 1.9% are defective, and 1.2% of the American chips are defective.Find the probability that a chip is defective. (Round your answer to four decimal places.)?

Answer:The probability is 0.0145.Step-by-step explanation:We first calculate two probabilities:the probability that a faulty chip is coming from Japan, denoted by P(D∪J), and the probability that a faulty chip is coming from the US, denoted by P(D∪A).And then we sum them up.Given that the probability of finding a defective chip is conditioned by the probabilities of the chips come from, we deduce that we'll have to use the formulae for extraction without replacement:P(D∪J) = P(J)*P(D/J)P(D∪A) = P(A)*P(D/A)We know that[tex]P(J) = 0.36\\ P(A)=0.64\\ P(D/J)=0.019\\ P(D/A)=0.012[/tex]So we can simply calculateP(D∪J)+P(D∪A) = [tex]P(J)*P(D/J)+P(A)*P(D/A)[/tex]P(D∪J)+P(D∪A) = [tex]0.36*0.019+0.64*0.012 = 0.01452[/tex]Therefore the rounded answer to 4 decimals would be 0.0145.