Chapter 3: Your computer stopped working some time ago, and today you are going

Question

Chapter 3: Your computer stopped working some time ago, and today you are going to the store to buy a new one. You narrowed you selection down to three brands: Apple, HP, and Lenovo. After researching these brands, you find that 4% of Apple computers are defective, 3% of HP computer are defective, and 2% of Lenovo computers are defective. Assuming that the probability of choosing any brand is the same, what is the probability that the computer you buy today is NOT defective? Moreover, what is the probability that you buy an Apple computer, given that it IS defective?

Explanation / Answer

1)P( not defective) =P(Apple and not defective+HP and not defective +Lenovo and not defective)

=(1/3)*(1-0.04)+(1/3)*(1-0.03)+(1/3)*(1-0.02)=0.97

2)

as P(defective) =1-P(not defective) =1-0.97 =0.03

therefore P(buy an Apple computer given defective) =P(Apple and defective)/P(defective) =(1/3)*0.04/0.03

=0.4444

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