Consider the following two lottery type games: Game 1: You pick one number between 1 and 50. After you have made your choice, a number between 1 and 50 is selected at random. If the selected number matches the number you picked, you win. Game 2: You pick two numbers between 1 and 10. After you have made your choices, two different numbers between 1 and 10 are selected at random. If the selected numbers match the two you picked, you win.
a. The cost to play either game is $ 1, and if you win you will be paid $ 20. If you can only play one of these games, which game would you pick and why? Use relevant probabilities to justify your choice.
b. For either of these games, if you plan to play the game 100 times, would you expect to win money or lose money overall? Explain.