(7) A particular concentration of a chemical found in polluted water has been found to he lethal to 20% of the fish that are exposed to the con-centration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. (a) Find the probability that exactly fourteen survive. (b) Find the probability that at least ten survive. (c) Find the mean and variance of the number that survive. (8) From an ordinary deck of 52 cards we draw cards at random, with re-placement. and successively until an ace is drawn. What is the probability that at least 10 drawn are needed ? (9) An absentminded professor, does not remember which which of his 8 keys will open his office door. If he tries them at random and with replacement: (a) On average, how many keys should he try before his door open ? (b) 1A'hat is the probability that he opens his office door after only three tries?