You opened a 3d printing start up, by acquiring 10 used industrial 3d printers. The previous owner informed you that 8 are working properly with only a 10% chance of producing noticeable defects and 2 that became defective resulting a 20% chance of producing noticeable defects. However, he forgot to label which printers are defective. (a) To test for a defective printer, you randomly select a printer and print 5 structures. If 2 of the 5 printed items is defectively printed, what is the probability that the chosen printer is defective.
(b) What is the probability that any given item printed by your start up is defective? (Assume that you do not know which machines are defective)