Phil is deciding which lottery scratch-off ticket to purchase. Below are his options. Lucky Ducky tickets cost $1 and offer this: Match three numbers in the correct order (using the numbers between 1 and 20) and win $500. Match 2 numbers and win $100. Match 1 number and win $20. Mega Bux tickets cost $5 and offer this: Match five numbers in the correct order (using the numbers between 1 and 100) and win $5000. Match 4 numbers and win $2000. Match 3 numbers and win $1000. Match 2 numbers and win $100. Match 1 number and win $50. Part A: Find the expected value for buying a Lucky Ducky ticket. Show all work. Part B: Find the expected value for buying a Mega Bux ticket. Show all work. Part C: Find the expected payoff for each game. Which ticket should Phil purchase? Explain.