A microcontroller manufacturer, Agduino, offers a single product which is produc

Question

A microcontroller manufacturer, Agduino, offers a single product which is produced at two different plants. The first plant located in college station produces 2/3 of the microcontrollers. The remaining microcontrollers come from Austin. A study shows that 1/10 of the microcontrollers coming out of College Station are defective. In contrast, the Austin plant has much looser standards and 2/5 of its microcontrollers are faulty.

a) What is the probability that an Agduino microcontroller comes from Austin?

b) What is the probability that a randomly selected Agduino microcontroller is defective?

c) If an Agduino microcontroller is defective, what is the probability that it was manufactured in Austin?

d) You purchased 3 Agduino microcontrollers and they are all faulty. What is the probability that at least one of them comes from college station?

Please Help! Explain how to derive the answer please, in order to understand.

Explanation / Answer

a) 1 - 2/3 = 1/3

b) (2/3)*(1/10) + (1/3)*(2/5) = 1/5

c) [ (1/3)*(2/5) ] / (1/5) = 2/3

d) 1 - (2/3)^3 = 19/27

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