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Sheau-Ru Tong, MISNPUST 3/4/2004 Homework 1 Due: 3/11/2004 11. A box has 10 balls numbered 1,2,…,10, A ball is picked at random and then a second ball is picked at random from the remaining nine balls. Find the probability that the numbers on the two selected balls differ by two or more. 13. Suppose we have four chests each having two drawers. Chests 1 and 2 have a gold coin in one drawer and a silver coin in the other drawer. Chest 3 has two gold coins and chest 4 has two silver coins. A chest is selected at random and a drawer opened. It is found to contain a gold coin. Find the probability that the other drawer has (a) a silver coin; (b) a gold coin. 14. A box has 10 balls, 6 of which are black and 4 of which are white. Three bal1 are removed from the box, their color unnoted. Find the probability that a fourth ball removed from the box is white. Assume that the 10 balls are equally likely to be drawn from the box. 20. Suppose a box has r red and b black balls. A ball is chosen at random from the box and then a second ball is drawn at random from the remaining balls in the box. Find the Probability that (a) both balls are red; (b) the first ball is red and the second is black; (c) the first ball is black and the second is red; (d) both balls are black. 22. Two balls are draw, with replacement of the first draw ball, from a box containing 3 white and 2 black balls. (a) Construct a sample space for this experiment with equally likely sample points. (b) Calculate the probability that both balls draw will be the same color. (c) Calculate the probability that at least one of the balls draw will white. 27. A college is composed of 70% men and 30% women. It is known that 40% of the men and 60%of the women smoke cigarettes. What is the probability that a student observed smoking a cigarette is a man? 37. Experience shows that 20% of the people reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes 52 reservations, what is the probability that it will be able to accommodate everyone?