The quality of each pair of photodiodes produced by the machine in Problem 1.7.6 is independent of the quality of every other pair of diodes.
(a) What is the probability of finding no good diodes in a collection of n pairs produced by the machine?
(b) How many pairs of diodes must the machine produce to reach a probability of 0.99 that there will be at least one acceptable diode?
Problem 1.7.6
A machine produces photo detectors in pairs. Tests show that the first photo detector is acceptable with probability 3/5. When the first photo detector is acceptable, the second photo detector is acceptable with probability 4/5. If the first photo detector is defective, the second photo detector is acceptable with probability 2/5.
(a) What is the probability that exactly one photo detector of a pair is acceptable?
(b) What is the probability that both photo detectors in a pair are defective?