1. A coin is tossed 25 times. The result is that there are 9 "heads" and 16 "tails". Consider the model that the number of "heads" follows a binomial distribution with the size equal to 25 and the probability of success equal to 0.5. That is, the probability of k 25 heads is computed as f (k) = (0.5)-. Denote this probability space by k binomial(25, 0.5). What is the probability of the event that the number of "heads" is less than or equal to 9 under the binomial(25, 0.5) model? Is the observed count of "heads" consistent with the hypothesis that the count follows a binomial(25, 0.5) distribution?2. Consider a deck of 5 cards labeled with the values 1 through 5. Suppose you shuffled the deck, draw one card, then another without replacing the first. You do this in such a way that any ordered pair of two distinct values (a, b) with {a, b } E { 1, 2,3, 4,5} is equally likely. Please define a reasonable probability space to model this experiment. You don't have to explain the model, just provide the values requested below. What is the probability of single outcome (a, b ) with a, b E {1, 2, 3, 4,5 }? What is the probability of the event { (a, b ) | a 2 2b)