Answer:
The expected value for the player is -$0.63.
Step-by-step explanation:
The dice game has the following rules:
- The game costs $3 to play.
- A player rolls two dice.
- If the player gets a sum of 2 or 12 he or she gets back $ 28 (wins $25).
- If the person gets a 7 he or she gets back $5 (wins $2).
- If the player rolls anything other than a 2, 12 or 7 he or she gets nothing back (loses $3).
The outcomes for a sum of 2 or 12 are: {(1, 1) and (6, 6)}
The probability of a sum of 2 or 12 is: 2/36 = 0.055.
The outcomes for a sum of 7 is: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}
The probability of a sum of 7 is: 6/36 = 0.167.
The probability of a sum other than 2, 12 or 7 is: 1 - 8/36 = 0.778
The probability distribution is:
Result X P (X)
Sum 2 or 12 $25 0.055
Sum 7 $2 0.167
Others -$3 0.778
Total 1.000
Compute the expected value as follows:
[tex]E(X)=\sum x\cdot P(x)\\\\[/tex]
[tex]=(25\times 0.055)+(2\times 0.167)+(-3\times 0.778)\\\\=1.375+0.334-2.334\\\\=-0.625\\\\\approx -0.63[/tex]
Thus, the expected value for the player is -$0.63.
