Problem 2 Suppose that (, P ) is a probabilistic model with = {n N n 10}. Assume also that P is a discrete uniform probability. Define the following events: A = {all even numbers in }, B = {multiples of 5 in }. Compute P(AB). (Hint: Use the inclusion-exclusion formula). How would your answer change if we changed the sample space to = {n N n 103}?

Problem 3 Consider the following experiment: There are 4 fair coins placed in a 2 2 matrix configuration. A trial consists of flipping each coin once and recording the resulting outcome as a binary 2 2 matrix where 0 signifies tails and 1 signifies heads. Derive a probabilistic model for this experiment. How many elements are in ?

Problem 4 For the experiment above, determine the probability that in at least one row (of the outcome matrix) all the entries are 1.

Problem 5 Consider the following experiment: A trial consists of repeatedly flipping a coin until heads is observed for the first time. Describe the sample space. Problem 6 Consider the following experiment: A trial consists of throwing a fair 6-sided