Peter Hopper, director of quality control for Harley Davidson, is conducting his weekly spot check of the transmission gear box of the newly introduced Wind Phantom series motorcycle. In this procedure, a random sample of 8 gear boxes are removed from the inventory pool of components and are checked for manufacturing. Historically, only 5% of the gear boxes have such flaws.

Assume that any flaws occur independently in different gear boxes.

a. What is the probability that Hopper's sample contains no gear boxes with manufacturing flaws?

b. What is the probability that Hopper's sample contains more than two gear boxes with manufacturing flaws?