1. White mice are employed to determine the effectiveness of a certain drug. If only 50% of the mice react to the drug, how many mice should be used to ensure that at least one of the mice will give an observable reaction with a probability of at least 95%
2. A men's store purchased a lot of 100 shirts from a certain manufacturere. Although 88 of the shirts were not damaged, the remaining shirts were not suitable to sell. A random sample of 40 shirts is chosen from the lot. Find the probability:
a. Exactly 36 shirts have not been damaged.
b. At most 22 shirts were not damaged.
Please show all work.