In Las Vegas casino, a pair of fair dice is rolled once, and the resulting sum determines if the player wins or loses the bet. Here are two methods of play: • Method 1: A $5 bet on under 7 (e.g., bet that the sum is less than 7: the player wins $5 if the sum is under 7 and loses $4 if the sum outcome is greater or equal than 7); • Method 2: A $5 bet on 7. For this bet, the player wins $8 if the result of the roll is 7 and loses 3$ otherwise. What is the expected profit (or loss) to the player, for each of the above method of play? Explain and present results with 4 decimals. Suppose a player rolls the dice 5 times. For Method 1, what is the probability that the player wins one time? For Method 1, what is the probability that the player wins three or more times? Present result with 4 decimals.
