A shipment of pins contains 25 good ones and 2 defective ones. At the receiving department, an inspector picks three pins at random and tests them. If any defective pin is found among the three that are tested, the shipment would be rejected.
a. What is the probability that the shipment would be accepted?
b. To increase the probability of acceptance to at least 90%, it is decided to do one of the following:
i. Add some good pins to the shipment.
ii. Remove some defective pins in the shipment.
For each of the two options, find out exactly how many pins should be added or removed.