A box contains 100 microchips, some of which were produced by factory 1 and the

Question

A box contains 100 microchips, some of which were produced by factory 1 and the rest by factory 2. Some of the Microchips are defective and some are good (nondefective). An experiment consists of choosing one microchip at random from the box and testing whether it is good or defective. Let the event A = "obtaining a defective microchip" and the event B = "the microchip was produced by factory 1". We know the number of microchips in each category (given in the table below). What is the probability of obtaining a defective microchip? What is the probability of obtaining a defective microchip that is produced by factory 1? What is the probability of obtaining a good microchip that is produced by factory 2? Find the probability that a defective microchip is selected given that the microchip was produced by factory 1. Find the probability that a defective microchip is selected given that the microchip was produced by factory 2.

Explanation / Answer

a) the probability is given by 20/100=20%

b) it is given by 15/100=15%

c) it is given by 35/100=35%

d) P(defective / produced by factory 1) =P(defective and produced by factory 1) /P(produced by factory 1)

= 15/60=25%

e)  P(defective / produced by factory 2) =P(defective and produced by factory 2) /P(produced by factory 2)

=5/40=12.5%

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