It is conjectured that an impurity exists in 30% of all drinking wells in a certain rural community. In order to gain some insight on this problem, it is determined that some tests should be made. It is too expensive to test all of the many wells in the area, so 10 were randomly selected for testing.
a. Using the binomial distribution, what is the probability that exactly three wells have the impurity assuming that the conjecture is correct?
b. What is the probability that more than three wells are impure?