1. Calculate the following probabilities. Justify your answeis (a) Suppose you flip a fair coin 3 times. What is the probobility of heads coening up exactly two times? (b) Suppose you toll two fair 6-sided dice and sum the numbers that appear. What is the probability of the sum being 9 ? (c) Suppose you foll two fair 6-sided dice and sum the numbers that appear. What is the probability of the sum being less than 6 ? (d) Suppose you roil two fair 8-sided dice and sum the numbers that appear. What is the probability of the sum being exactly 2 ? (0) Suppose you roll two fair 6-sided dice and sum the numbers that appeag. What is the probability of the complement of the sum being greater than 10? 2. Calculate the expected value for the folowing game and give the probability of each outcome occurring. Determine whether the house or the player has the advantage Justify your answers In this game the player is asked to roll two 6-sided dice and sum the numbers appearing, It costs 33 to play the game. If the sum is a 6 , 7 or 8 the player gets $3 and the cost to play the game is returned (that is, the payoff is $6 ). If the sum is 12 the player gets $10 and the cost to play is returned. Otherwise the player loses the $3 it cost to play. 3. Calculate the following statistical measures for the exam scores ghen belowr, the data has a mean of 80.75. You can check your answers uving Python for your scientific calculator) but the formulas for each must be written down. Justify your answers 81,72,95,85,76,71,81,76 (a) Determine the medan of the data. (b) Determine the variance of the data. Note: use the formula for data variance, that is divide by the number of data points minas one. (c) Determine the standard deviation for the data