Expected Value Practice

A $20 bill, two $10 bills, three $5 bills and four $1 bills are placed in a bag. If a bill is chosen at random, what is the expected value for the amount chosen?

In a game you flip a coin twice, and record the

number of heads that occur. You get 10

points for 2 heads, zero points for 1 head, and

5 points for no heads. What is the expected

value for the number of points you'll win per turn?

There is an equally likely chance that a falling dart will land anywhere on the rug above. The following system is used to find the number of points the player wins. What is the expected value for the number of points won? Black = 40 points Gray = 20 points White = 0 points

A mysterious card-playing squirrel (pictured) offers you the opportunity to join in his game. The rules are: To play you must pay him $2. If you pick a spade from a shuffled pack, you win $9. Find the expected value you win (or lose) per game.

A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.

A raffle is held by the MTHS ASB to draw for a $1000 plasma television. Two thousand tickets are sold at $1.00 each. Find the expected value of one ticket.

A game consists of flipping two coins. If both coins turn up heads, you win $1.00. What is a "fair" price to pay to play? (What is the expected value of one play?)

A game consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is a "fair" price to pay to play? (What is the expected value of one play?)

A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. Would you play the game? Why or why not?

Suppose you were given one of thirty free tickets at the beginning of this class period. Suppose at the end of this period, three tickets are drawn without replacement. The holder of the first ticket drawn wins $100, the second ticket $50, and the third ticket $30. (a) Determine your expected winnings. (b) If your neighbor offered to buy your ticket before drawing, what would be a "fair price"?