1. Consider a random experiment where a fair die is rolled repetitively until a one is observed. The total number of rolls is recorded as the outcome of this experiment and, as such, the sample space is 2 = {1, 2, ...}. (a) 1 pt - What is the probability of observing one on the first trial? (b) 1 pt - What is the probability of having to roll the die exactly k times to see a one? (c) 1 pt - Compute the probability that the number of rolls is even? (d) 1 pt - For this part, suppose that you roll a fair die repetitively until you observe a one twice. What is the probability of observing one for the second time on the fourth trial? (e) 1 pt - For this part, suppose that you roll a fair die repetitively until you see a one three times. For & > 3, find a formula for the probability that you see a one for the third time exactly on the kth roll