Gears produced by a grinding process are categorized either as conforming (suitable for their intended purpose), downgraded (unsuitable for the intended purpose but usable for another purpose), or scrap (not usable). Suppose that 80% of the gears produced are conforming, 15% are downgraded, and 5% are scrap. Ten gears are selected at random.

a. What is the probability that one or more is scrap?

b. What is the probability that eight or more are not scrap?

c. What is the probability that more than two are either downgraded or scrap?

d. What is the probability that exactly nine are either conforming or downgraded?