4. You have four boxes. Box I contains 2000 components of which 200 are defectiv

Question

4. You have four boxes. Box I contains 2000 components of which 200 are defective, box II contains 1200 components of which 200 are defective, box III contains 1200 components of which 100 are defective, box IV contains 1000 components of which 100 are defective. You select the first box with probability 3, the second box with probability .2, the third with probability 3 and remove at random a single component. a) what is the probability that the selected component is defective? 7p b) You examine the selected component and find it defective. What is probability 8p that it came from box III?

Explanation / Answer

a)probability that selected component is defective=P( box I selected and component defective+box II selected and component defective+box III selected and component defective+box IV selected and component defective)

=0.3*(200/2000)+0.2*(200/1200)+0.3*(100/1200)+0.2*(100/1000)=0.1083

b)probability it came from box III given defective =P(box III selected and component defective)/P(defective)

=0.3*(100/1200)/0.1083 =0.2308

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