A computer chip can be one of the two types: Defective (D) or Not-Defective (ND)

Question

A computer chip can be one of the two types: Defective (D) or Not-Defective (ND). Give a chip, however, there is no easy way to tell whether is defective, but there is a test that can be applied to decide: the test give + results, identifying the chip as defective, with probability 0.9 if the chip is defective, and + result with probability 0.1 if the chip is not-defective. I randomly select a ship from a population in which there are 10 defective and 990 not-defective chips, apply the test on this selected chip, and get a + results. What is the probability that the chip is actually defective?

Explanation / Answer

probabilty of getting (+) result =(Probabilty chip ND and got + results)+ (chip D and got +results)

=(990/1000)*0.1+(10/1000)*0.9=0.108

hence  probability that the chip is actually defective given test is +ve

=results+chip D and got +results/probabilty of getting (+) result =(10/1000)*0.9/0.108=0.0833

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