A shipment of assembly parts from a vendor offering inexpensive parts is used in a manufacturing plant. The box of 12 parts contains 5 that are defective and will not ft during assembly. A worker picks parts one at a time and attempts to install them. Find the probability of each outcome.
(a) The first two chosen are both good.
(b) At least one of the first three is good.
(c) The first four picked are all good.
(d) The worker has to pick five parts to find one that is good.