The random variable X can take values 1 and 2, and the random variable Y takes values from the set {1, 2, ..., a} with a =4. The joint probability mass function of X and Y is given by the following function: p(x, y) = c(a + 1) where c is a positive constant, a E {1, 2}, y E {1, 2, ..., a}. Find the probability P(Y = 4). Provide a numerical answer with precision up to 3 decimal places. Question 2 1 pts For each lecture the professor chooses between white, yellow, and purple chalk uniformly at random, independently of previous choices. What is the probability that over the next 6 days she will choose white chalk 1 times, yellow chalk 1 times, and purple chalk the remaining times? Provide a numerical answer with precision up to 3 decimal places