Final answer:
The probability of rolling three primes and three composites on six 6-sided dice is 25 / 2916.
Step-by-step explanation:
To find the probability of rolling three primes and three composites on six 6-sided dice, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Calculate the number of ways to roll three primes on six dice. There are three prime numbers on a 6-sided die: 2, 3, and 5. So, the number of ways to choose three primes from six is given by the combination formula: C(6, 3) = 6! / (3!(6-3)!) = 20.
2. Calculate the number of ways to roll three composites on six dice. There are three composite numbers on a 6-sided die: 4, 6. So, the number of ways to choose three composites from six is also 20.
3. Calculate the total number of possible outcomes when rolling six dice. On each die, there are six possible outcomes, so the total number of outcomes is 6^6 = 46656.
4. Finally, calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: P = (20 * 20) / 46656 = 400 / 46656 = 25 / 2916.