Question

Expected Value (50 points) Game: Roll two dice. Win a prize based on the sum of the dice. Cost of playing the game: $1 Prizes: Win $10 if your sum is odd. Win $5 if you roll a sum of 4 or 8. Win $50 if you roll a sum of 2 or 12. Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)

Answer 1

$7.89

Explanation:

There are 36 possible outcomes when rolling two dice.

The sum will be odd if the first die is odd and the second is even or if the second is odd and the first is even. The probability of an odd sum is:

`P(odd)=(3)/(6) *(3)/(6) +(3)/(6) *(3)/(6)\\P(odd)=0.5`

There is a probability of 1 in 2 of winning $10.

There are 8 ways to get a sum of 4 or 8 (1,3; 3,1; 2,2; 5,3; 3,5; 2,6; 6,2; 4,4). There is a probability of 8 in 36 or 2 in 9 of winning $5.

There are 2 ways to get a sum of 2 or 12 (1,1; 6,6). There is a probability of 2 in 36 or 1 in 18 of winning $50.

Any other outcome will not payout any amount.

The expected value is the sum of all possible payouts multiplied by their likelihood (including a 100% chance of paying $1 to play).

`E=-1+10*(1)/(2) +5*(2)/(9)+50*(1)/(18)\\E=\$7.89`

The expected value is $7.89.