When six standard six-sideddice are rolled,what is the most likely sums of the six number?
To determine the most likely sums when rolling six standard six-sided dice, we need to consider the possible outcomes and their probabilities.
Each six-sided die has six possible outcomes: 1, 2, 3, 4, 5, or 6. When rolling multiple dice, we can find the sums by adding up the outcomes of each die.
To calculate the probabilities, we need to consider the number of ways each sum can occur. For example, there is only one way to get a sum of 6 (rolling six ones), but there are multiple ways to get a sum of 7 (rolling a one and a six, a two and a five, etc.). We can use combinatorics to help determine the number of ways each sum can occur.
Here are the possible sums and their corresponding probabilities:
Sum of 6: There is only one way to get a sum of 6 (rolling six ones). Probability = 1/(6^6).
Sum of 7: There are six ways to get a sum of 7 (rolling a one and a six, a two and a five, etc.). Probability = 6/(6^6).
Sum of 8: There are 21 ways to get a sum of 8. Probability = 21/(6^6).
Sum of 9: There are 56 ways to get a sum of 9. Probability = 56/(6^6).
Sum of 10: There are 126 ways to get a sum of 10. Probability = 126/(6^6).
Sum of 11: There are 252 ways to get a sum of 11. Probability = 252/(6^6).
Sum of 12: There are 462 ways to get a sum of 12. Probability = 462/(6^6).
Now, to determine the most likely sums, we compare their probabilities. The sum with the highest probability is the most likely sum.
By calculating the probabilities, we find that the most likely sum of the six numbers rolled on the six-sided dice is 7, followed by 8, 9, 6, 10, 11, and 12 in decreasing order of likelihood.