1.  Consider the experiment, called the birthday problem , where our task is to determine the probability that in a group of people of a certain size there are a least two people who have the same birthday (the same month and day of month). Suppose there is a room with 12 people in it, find the probability that at least two people have the same birthday.

2. Suppose that 6 dice thrown are thrown and the number, N, of spots showing is noted. Then suppose N coins are tossed, what is the expected number of heads? Expected number of heads =  

3. The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which have the capacity to damage the computer. The amount of damage to the computer depends on the strength of the surge. It has been estimated that there is a 2% chance of incurring 450 dollar damage, 6% chance of incurring 150 dollar damage, and 12% chance of 150 dollar damage. An inexpensive suppressor, which would provide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value?