-In a lottery game, a player picks six numbers from 1 to 25. If the player matches all six numbers, they win 30,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

-In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

-In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 20,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

-In a lottery game, a player picks six numbers from 1 to 30. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.

What is the expected value of this game?

-A bag contains 2 gold marbles, 6 silver marbles, and 25 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?

-A bag contains 2 gold marbles, 10 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?

-A bag contains 1 gold marbles, 6 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.

What is your expected value if you play this game?