Problem 2. Consider the following chance game: 0 Two fair, six-sided dice are rolled. One die is red while the other is blue. The two dice have independent outcomes from each other. (Note: a single sixsided die roll takes on values in the Set {1: 2: 31 415?6}') o If the red die rolls a 1 or a 2, you win $0 regardless of what is rolled on the blue die. 0 If the red die rolls a 3 or higher, you win $16 where k is the number rolled on the blue die. Dene the discrete random Variable X to be the winnings from playing this game once. a) State the sample space of the random variable X. (210%) b) State the probability mass function of the random variable X. State the probabilities as exact fractions. (6pts) c) Suppose the game costs $2 to play. Is this a favourable game to the player? Justify your answer. (4N8)