Question

Three dice are rolled. Let the random variable x represent the sum of the 3 dice. By assuming that each of the 63 possible outcomes is equally likely, find the probability that x equals 11.

Answer 1

Answer:  1/8

In decimal form, 1/8 = 0.125 which converts to 12.5%

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Work Shown:

The 63 should be 6^3. There are 6 choices per slot, and 3 slots, so 6^3 = 216 different outcomes.

Here are all of the ways to add to 11 if we had 3 dice

1. sum = 1+4+6 = 11
2. sum = 1+5+5 = 11
3. sum = 1+6+4 = 11
4. sum = 2+3+6 = 11
5. sum = 2+4+5 = 11
6. sum = 2+5+4 = 11
7. sum = 2+6+3 = 11
8. sum = 3+2+6 = 11
9. sum = 3+3+5 = 11
10. sum = 3+4+4 = 11
11. sum = 3+5+3 = 11
12. sum = 3+6+2 = 11
13. sum = 4+1+6 = 11
14. sum = 4+2+5 = 11
15. sum = 4+3+4 = 11
16. sum = 4+4+3 = 11
17. sum = 4+5+2 = 11
18. sum = 4+6+1 = 11
19. sum = 5+1+5 = 11
20. sum = 5+2+4 = 11
21. sum = 5+3+3 = 11
22. sum = 5+4+2 = 11
23. sum = 5+5+1 = 11
24. sum = 6+1+4 = 11
25. sum = 6+2+3 = 11
26. sum = 6+3+2 = 11
27. sum = 6+4+1 = 11

There are 27 ways to add to 11  using 3 dice. This is out of 216 total outcomes of 3 dice being rolled.

So, 27/216 = (1*27)/(8*27) = 1/8 is the probability of getting 3 dice to add to 11.