Download Queueing Theory: Mid

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?