Question 1.(5 marks) In a game, two 6-sided dice (with the numbers 1-6 on the faces of each die) are rolled, and the player bets on the appearance of a particular number. One die is a fair die, meaning that each face has the same probability of landing face up. The other die is not fair. Instead, each of the odd numbers 1, 3, and 5 have a probability of landing face up, while each of the even numbers 2, 4 and 6 have a probability of landing face up. The player wins $2 if their number appears on exactly one die, and $4 if their number appears on both dice. They lose $1 if their number doesn't appear on either die. (a) A player, Himal, really likes low numbers, so much so, that he will always choose a low number to bet on in this game, and is equally likely to choose either 1, 2 or 3. Calculate Himal's expected average win. (b) On average, can Himal expect to make money by playing this game? (c) Another player - Himal's sister, Hazel - really likes high numbers, so much so, that she will always choose a high number to bet on in this game, and is equally likely to choose either 4, 5 or 6. How much more, on average, is Himal expected to win, compared to his sister?