Use expected value to judge whether a game is fair

Question 1

A charity game costs 2 to play. The chance of winning is 0.1 and the prize is 19 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 2

It costs $3 to play. You roll a fair die and win $3 if you roll a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 3

A charity game costs 3 to play. The chance of winning is 0.1 and the prize is 32 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 4

It costs $3 to play. You roll a fair die and win $3 if you roll a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 5

A charity game costs 3 to play. The chance of winning is 0.25 and the prize is 12 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 6

It costs $1 to play. You roll a fair die and win $6 if you roll a 5 or a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 7

A charity game costs 4 to play. The chance of winning is 0.25 and the prize is 15 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 8

It costs $1 to play. You roll a fair die and win $6 if you roll a 5 or a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 9

A charity game costs 3 to play. The chance of winning is 0.1 and the prize is 30 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 10

It costs $2 to play. You roll a fair die and win $3 if you roll a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 11

A charity game costs 3 to play. The chance of winning is 0.5 and the prize is 8 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 12

It costs $3 to play. You roll a fair die and win $3 if you roll a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 13

A charity game costs 4 to play. The chance of winning is 0.1 and the prize is 40 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 14

It costs $2 to play. You roll a fair die and win $6 if you roll a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 15

A charity game costs 3 to play. The chance of winning is 0.25 and the prize is 11 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 16

It costs $1 to play. You roll a fair die and win $3 if you roll a 5 or a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer