1) A shipment contains 20 assembled circuit boards of which are five are defective. Ten circuit boards from the shipment are selected without replacement. Suppose X denotes the number of defective boards out of the 10 selected. Find the probability distribution of the random variable X and then find its mean and variance
2) An IRS inspector randomly selects five persons from a group of 20 who are potential candidates to be audited. Of the 20 persons, nine were audited in the past, while the other 11 have never been audited before. Find the probability that the number of persons selected who were audited in the past is
(a) Exactly three
(b) More than two
(c) At least two
(d) at most three