Answer :
To find the probability of obtaining a sum not greater than 16 when rolling 3 fair dice, we first calculate the total number of possible outcomes when rolling three dice. Each die has 6 faces, so:
Total outcomes = \( 6 \times 6 \times 6 = 216 \)
Next, we determine how many outcomes result in a sum not greater than 16. The possible sums range from 3 (when all dice show 1) to 18 (when all dice show 6).
We need to count the outcomes where the sum is 16 or less:
- **Sum = 3:** (1,1,1) → 1 way
- **Sum = 4:** (1,1,2), (1,2,1), (2,1,1) → 3 ways
- **Sum = 5:** (1,1,3), (1,2,2), (2,1,2), (2,2,1), (1,3,1), (2,3,1), (3,1,1) → 7 ways
- **Sum = 6:** (1,1,4), (1,2,3), (1,3,2), (1,4,1), (2,1,3), (2,2,2), (2,3,1), (3,1,2), (3,2,1), (4,1,1) → 10 ways
- **Sum = 7:** ... Continue this pattern up to sum 16
Instead of counting all manuallyAnswer:
Step-by-step explanation:
