1. (12 points) A very large batch component has arrived at a distributor. 10% of the components in the batch are defective but the distributor does not know the exact percentage of the defective components. He decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2.

a. What is the probability that the batch will be accepted?

b. What is the probability that among 10 components, 5 of them are defective?

c. What is the probability that among 10 components, 3 or 4 of them are defective?