Question

a. 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 1.4% of the American chips are defective.

Find the probability that a chip is defective and made in Japan. (Round your answer to four decimal places.)

b. A personal computer manufacturer buys 38% of its chips from Japan and the rest from the United States. Of the Japanese chips, 1.5% are defective, and 1.3% of the American chips are defective.

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

Answer 1

Solution :

Probability that a chip is from Japan = 36% = 0.36.

Probability that the chip is from U.S. = 1 - 0.36 = 0.64.

Probability that a Japanese chip is defective = 1.7% = 0.017.

Probability that a U.S. chip is defective = 1.3% = 0.013.

=> Probability that a chip is defective = 0.32 * 0.017 + 0.68 * 0.013 = 0.02532

Probability that a chip is from Japan = 38% = 0.38.

Probability that the chip is from U.S. = 1 - 0.38 = 0.62.

Probability that a Japanese chip is defective = 1.5% = 0.015.

Probability that a U.S. chip is defective = 1.3% = 0.013.

=> Probability that a chip is defective = 0.38 * 0.015 + 0.6 * 0.013 = 0.01376

=> Probability that a chip is defect free = 1 - 0.01376 = 0.9862.

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