Questions. Answers are below.
1. A game costs $10 to play. Roll a 6 sided die. If a 5 is rolled, you win $30. Find the EV and explain if this is a good game to play.
2. A game costs $3 to play. A number 1 - 100 is chosen. If a 7 is chosen, you win $100. Find the EV and explain if this is a good game to play.
3. Create a tree where the odds of each are as follows: A = 1/2, B = 1/8, C = 1/8, D= 1/4
4. A game costs $5 to play. A card is chosen off the top of a deck of cards. If it is red, you win $6. Find the EV and explain if this is a good game to play.
5. Create a tree where the odds are as follows: A = 1, B=0
6. A game costs $20 to play. A die is rolled. Take the value of the die (for example a 4) and multiply it by $5. (so a 4 is $20). Find the EV and explain if this is a good game to play.
Answers:
1. (1/6)*20 + (5/6)*(-10) = -5 EV. This is not a good game to play.
2. (1/100)*(97) + (99/100)*(-3) = -2 EV. This is not a good game to play.
3. Check your notes from class, we did one exactly like this.
4. (1/2)*(1) + (1/2)(-5) = -2 EV. This is yet another terrible game to play.
5. Have a line pointing to A. Have no lines pointing at B.
6. (1/6)*(-15) + (1/6)*(-10) + (1/6)*(-5) +(1/6)*(0) + (1/6)*(5) + (1/6)*(10) = -2.5 EV. All of these have been bad games to play. Your quiz should have one that's good to play, so be prepared.