Probability w/computer chips

Question

(a)A personal computer manufacturer buys 38% of its chips from Japan and the rest from the United States. Of the Japanese chips, 1.7% are defective, and 1.1% of the American chips are defective.

Find the probability that a chip is defect-free. (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, 1.8% are defective, and 1.1% of the American chips are defective.

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

Answer 1

Answers:

a) Note that P_df is the probabilty that a chip is defect-free, P_dfJ is the probability that a chip is defect-free from Japan and P_dfUSA is the probablity that a chip is defect-free from USA.

P_df = P_dfJ+ P_dfUSA

= (1-1.7%)*38% + (1-1.1%)*(1-38%)

= 98.67%

So the probabilty that a chip is defect-free is 98.67%

b) Note that P_d is the probability that a chip is defective, P_dJ is the probability that a chip is defective and from Japan and P_dUSA is the probability that a chip is defective and from USA.

P_d = P_dJ + P_dUSA

= 1.8%* 38% + 1.1%*(1-38%)

= 1.37%

So the probabilty that a chip is defective is 1.37%