a student rolls three standard six-sided dice. what is the probability that the sum of the numbers that come up will be 18? is the answer 1/216
Yes
To find the probability of getting a sum of 18 when rolling three standard six-sided dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
To get a sum of 18, we can have the following combinations:
- 6, 6, 6
Since there is only one favorable outcome, the number of favorable outcomes is 1.
Now, let's calculate the total number of possible outcomes. Each dice has 6 sides, and we are rolling three dice, so the total number of possible outcomes is 6^3 = 216.
Therefore, the probability of getting a sum of 18 is:
Number of favorable outcomes / Total number of possible outcomes = 1 / 216.
So, yes, the answer is 1/216.
To find the probability of rolling dice and getting a sum of 18, we first need to determine the total number of possible outcomes. For each of the three dice, there are 6 possible outcomes since each die has 6 sides.
To find the total number of outcomes, we use the concept of counting principle. Since each die has 6 possible outcomes, the total number of outcomes is calculated as 6^3 = 216.
Now we can determine the number of successful outcomes, which in this case is rolling the dice and obtaining a sum of 18. We need to count the number of combinations of three numbers (representing each die) that add up to 18.
Possible combinations to get a sum of 18:
- 6 + 6 + 6
Therefore, there is only 1 successful outcome.
Finally, we can calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes:
Probability = Number of successful outcomes / Total number of possible outcomes
Probability = 1 / 216
So, the correct answer is 1/216.