Final answer:
To approximate the probability, we can use generating functions to find the number of favorable outcomes and total possible outcomes. We divide the number of favorable outcomes by the total number of possible outcomes to find the probability.
Step-by-step explanation:
To approximate the probability that the sum of the values obtained from rolling 10 fair dice is between 30 and 40 (inclusive), we need to find the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes are the combinations of numbers on the dice that sum up to a value between 30 and 40. Since there are 10 dice and each die has 6 sides, we can use the concept of generating functions to simplify the calculation. We can represent the dice as a polynomial with 6 terms, each representing the possible outcomes on the die (x^1 for a 1, x^2 for a 2, and so on, up to x^6 for a 6).
By raising this polynomial to the power of 10, we can find the coefficients of the resulting polynomial that represent the sums of the values obtained. We then sum up the coefficients from x^30 to x^40 to find the total number of favorable outcomes.
Finally, we divide the number of favorable outcomes by the total number of possible outcomes (6^10) to find the probability.