Question

: 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 1

Answer: 0.9862

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

`P(D)=P(D|J)* P(J)+P(D|U)* P(U)\\\\\Rightarrow\ P(D)=0.017*0.36+0.012*0.64=0.0138`

Thus , the probability that chip is defective = 0.0138

Then , the probability that a chip is defect-free=
`1-0.0138=0.9862`