When a six-sided dice numbered1,2,3,4,5and 6 is rolled many times until thesum is greater than12,what is the least likely sum?
To determine the least likely sum when rolling a six-sided dice until the sum is greater than 12, we can calculate the probabilities of all possible sums.
First, let's consider the possible sums individually:
- If we roll a 1, the sum would stay at 1.
- If we roll a 2, the sum would become 2.
- If we roll a 3, the sum would become 3.
- If we roll a 4, the sum would become 4.
- If we roll a 5, the sum would become 5.
- If we roll a 6, the sum would become 6.
- If we roll a 1 again, the sum would become 1 + 1 = 2.
- If we roll a 2 again, the sum would become 2 + 2 = 4.
- If we roll a 3 again, the sum would become 3 + 3 = 6.
- If we roll a 4 again, the sum would become 4 + 4 = 8.
- If we roll a 5 again, the sum would become 5 + 5 = 10.
- If we roll a 6 again, the sum would become 6 + 6 = 12.
- If we roll a 1 for the third time, the sum would become 2 + 1 = 3.
- If we roll a 2 for the third time, the sum would become 4 + 2 = 6.
- If we roll a 3 for the third time, the sum would become 6 + 3 = 9.
- If we roll a 4 for the third time, the sum would become 8 + 4 = 12.
- If we roll a 5 for the third time, the sum would become 10 + 5 = 15.
- If we roll a 6 for the third time, the sum would become 12 + 6 = 18.
As we can see, once the sum reaches 13 or higher, it will not go back to any of the lower sums. Therefore, the least likely sum would be 13.
To summarize, the least likely sum when rolling a six-sided dice until the sum is greater than 12 is 13.