lenamitkova
New member
- Joined
- Dec 14, 2021
- Messages
- 3
Hello, I am writing to you in connection with one of the sample assignments I was given for homework. I tried several times to calculate it, but to no avail. I have calculated all possible combinations when throwing the sums from 3 to 18 points and their percentages and probabilities, but I cannot reach a final solution to the problem. I will be infinitely grateful to you! - A gambling game is played in which a player bets $ 10 the bank and rolls three dice. If a six falls, the bank returns it pledge. For two sixes, the bank pays the player $ 50, and for three - $ 250. What is the average profit of the player? I've come this far:
3 = 1 + 1 + 1
4 = 1 + 1 + 2
5 = 1 + 1 + 3 = 2 + 2 + 1
6 = 1 + 1 + 4 = 1 + 2 + 3 = 2 + 2 + 2
7 = 1 + 1 + 5 = 2 + 2 + 3 = 3 + 3 + 1 = 1 + 2 + 4 8 = 1 + 1 + 6 = 2 + 3 + 3 = 4 + 3 + 1 = 1 + 2 + 5 = 2 + 2 + 4 9 = 6 + 2 + 1 = 4 + 3 + 2 = 3 + 3 + 3 = 2 + 2 + 5 = 1 + 3 + 5 = 1 + 4 + 4
10 = 6 + 3 + 1 = 6 + 2 + 2 = 5 + 3 + 2 = 4 + 4 + 2 = 4 + 3 + 3 = 1 + 4 + 5
11 = 6 + 4 + 1 = 1 + 5 + 5 = 5 + 4 + 2 = 3 + 3 + 5 = 4 + 3 + 4 = 6 + 3 + 2
12 = 6 + 5 + 1 = 4 + 3 + 5 = 4 + 4 + 4 = 5 + 2 + 5 = 6 + 4 + 2 = 6 + 3 + 3 13 = 6 + 6 + 1 = 5 + 4 + 4 = 3 + 4 + 6 = 6 + 5 + 2 = 5 + 5 + 3 14 = 6 + 6 + 2 = 5 + 5 + 4 = 4 + 4 + 6 = 6 + 5 + 3 15 = 6 + 6 + 3 = 6 + 5 + 4 = 5 + 5 + 5 16 = 6 + 6 + 4 = 5 + 5 + 6 17 = 6 + 6 + 5 18 = 6 + 6 + 6 3: 1/216 = 0.5% 4: 3/216 = 1.4% 5: 6/216 = 2.8% 6: 10/216 = 4.6% 7: 15/216 = 7.0% 8: 21/216 = 9.7% 9: 25/216 = 11.6% 10: 27/216 = 12.5% 11: 27/216 = 12.5% 12: 25/216 = 11.6% 13: 21/216 = 9.7% 14: 15/216 = 7.0% 15: 10/216 = 4.6% 16: 6/216 = 2.8% 17: 3/216 = 1.4% 18: 1/216 = 0.5%
3 = 1 + 1 + 1
4 = 1 + 1 + 2
5 = 1 + 1 + 3 = 2 + 2 + 1
6 = 1 + 1 + 4 = 1 + 2 + 3 = 2 + 2 + 2
7 = 1 + 1 + 5 = 2 + 2 + 3 = 3 + 3 + 1 = 1 + 2 + 4 8 = 1 + 1 + 6 = 2 + 3 + 3 = 4 + 3 + 1 = 1 + 2 + 5 = 2 + 2 + 4 9 = 6 + 2 + 1 = 4 + 3 + 2 = 3 + 3 + 3 = 2 + 2 + 5 = 1 + 3 + 5 = 1 + 4 + 4
10 = 6 + 3 + 1 = 6 + 2 + 2 = 5 + 3 + 2 = 4 + 4 + 2 = 4 + 3 + 3 = 1 + 4 + 5
11 = 6 + 4 + 1 = 1 + 5 + 5 = 5 + 4 + 2 = 3 + 3 + 5 = 4 + 3 + 4 = 6 + 3 + 2
12 = 6 + 5 + 1 = 4 + 3 + 5 = 4 + 4 + 4 = 5 + 2 + 5 = 6 + 4 + 2 = 6 + 3 + 3 13 = 6 + 6 + 1 = 5 + 4 + 4 = 3 + 4 + 6 = 6 + 5 + 2 = 5 + 5 + 3 14 = 6 + 6 + 2 = 5 + 5 + 4 = 4 + 4 + 6 = 6 + 5 + 3 15 = 6 + 6 + 3 = 6 + 5 + 4 = 5 + 5 + 5 16 = 6 + 6 + 4 = 5 + 5 + 6 17 = 6 + 6 + 5 18 = 6 + 6 + 6 3: 1/216 = 0.5% 4: 3/216 = 1.4% 5: 6/216 = 2.8% 6: 10/216 = 4.6% 7: 15/216 = 7.0% 8: 21/216 = 9.7% 9: 25/216 = 11.6% 10: 27/216 = 12.5% 11: 27/216 = 12.5% 12: 25/216 = 11.6% 13: 21/216 = 9.7% 14: 15/216 = 7.0% 15: 10/216 = 4.6% 16: 6/216 = 2.8% 17: 3/216 = 1.4% 18: 1/216 = 0.5%