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?