A factory finds that, on average, 20% of the bolts produced by a given machine will be defective for certain specified requirements. If 10 bolts are selected at random from the day's production of this machine, find the probability (a) that 2 or more will be defective and (b) that more than 5 will be defective. If the probability that an individual will suffer a bad reaction from injection of a given serum is 0.001, determine the probability that out of 2000 individuals, more than 2 individuals will suffer a bad reaction. The contents of two boxes used for storing hydrometers in the stockroom have become mixed. Box A, which is easier to reach and thus gone into by 2/3 of the students, contains 6 API hydrometers and 4 Baume hydrometers. Box B contains 10 hydrometers, of which 5 are Baume and 5 are API hydrometers. (a) If you remove one from each box, what is the probability that the two selected will be of the same type? (b) What is the probability that a second hydrometer removed from one of the boxes will be of the same type as the one initially removed from that box? A box contains 8 red, 3 white, and 9 blue marbles. If 3 balls are drawn at random, determine the probability that (a) 2 are red and 1 is white, (b) at least 1 is white, and (c) 1 of each color is drawn.