Question

-. For the event of rolling three standard fair 6-sided dice, find the following probabilities. Give all

answers as a simplified fraction.
The probability of rolling a sum of 8 or a sum of 12.
P(Sum is 8 u Sum is 12)

Answer 1

23/108

Explanation:

Remark

• There are 6 * 6 * 6 = 216 ways that you can throw three dice.
• There are 21 different ways of throwing an 8
• There are 25 different ways of throwing a 12
• I'll list the eights. The 12s are done the same way.

Ways of making Eight

1. 116
2. 125
3. 134
4. 143
5. 152
6. 161
7. 215
8. 224
9. 233
10. 242
11. 251
12. 314
13. 323
14. 332
15. 341
16. 413
17. 422
18. 431
19. 512
20. 521
21. 611

Answer

P(8) = 21 / 216

P(12) = 25/ 216

P(8 or 12) = 21/216 + 25/216

P(8 or 12) = 46/216 = 23/108