The director of quality 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 defects. Historically, only 5% of the gear boxes have such flaws. Any flaws occur independently in different gear boxes.
A.) What is the probability that the director of quality's sample contains no gear boxes with manufacturing flaws?
B.) What is the probability that the director of quality's sample contains more than two gear boxes with manufacturing flaws?