Final answer:
The probability of obtaining certain sums when rolling three dice with one die showing a 5 is calculated by identifying the possible outcomes for the other two dice and dividing by the total possible outcomes. Some sums have a higher number of combinations, and one sum, 18, cannot be achieved.
Step-by-step explanation:
The student is asking about the probability of obtaining certain sums when rolling three dice, with one die already showing a 5. To calculate the probability for each sum (i), we first determine the possible outcomes of the remaining two dice that would lead to the desired sum when added to 5. We then divide the number of favorable outcomes by the total number of possible outcomes when rolling two six-sided dice (36).
- For a sum of 7: There is only 1 combination (5+1+1), so the probability is 1/36.
- For a sum of 10: There are 3 combinations (5+3+2, 5+4+1, 5+2+3), so the probability is 3/36 or 1/12.
- For a sum of 15: There are 4 combinations (5+5+5, 5+6+4, 5+4+6, 5+6+4), so the probability is 4/36 or 1/9.
- For a sum of 16: There is 1 combination (5+6+5), so the probability is 1/36.
- For a sum of 18: It's impossible to achieve this sum with one die showing a 5, so the probability is 0.
Notice that some sums, like 18, cannot be attained given the constraints, while others have a higher number of combinations, affecting the probability