1. Consider the experiment of placing two distinguishable particles a and b into three cells. Examples of outcomes are w = : (ab|- |-), w = (a|b|-), etc. (a) Write down the sample space . (b) Define the following events: A: Two cells are occupied. B: The middle cell is not occupied. C: Both A and B occur. Identify the outcomes in each event A, B, and C. (c) Assume equal probability for each outcome. Calculate the probability of events A, B, and C. 2. Consider a similar experiment as in Problem 1, but with two indistinguishable particles denoted by *. Examples of outcomes are wi (** | - |-), w = : (*|*|-), etc. Repeat the parts of Problem 1 in this new experiment setting. =