Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (-$1).

a. Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table.

b. What is Miguel’s expected value from playing the game?

c. Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays?

d. What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.