Question: Consider rolling a pair of fair dice.

a) What is the probability that the number of dots on the upward side of both dice is the same (i.e., you roll (1,1) or (2,2) or (3,3) or (4,4) or (5,5) or (6,6))? [Note: we'll call this a matched roll in the remainder of this question.]

b) What is the probability that there is matched roll among the first 6 rolls?

c) Find the expectation and the standard deviation of the number of rolls you need to do until you have a matched roll (the final matched roll is included in the count)?