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Question: Jackson rolls four fair 6-sided dice, each numbered from 1 to 6. What is the probability that exactly two of the dice show a prime number?
We want exactly 2 dice to show a prime. This is a binomial probability:
Now convert all to denominator $156250$ for consistency:
Now convert all to denominator $15625$:
Total favorable: $4096 + 4913 + 4913 + 27744 = 41666$
But simplify: divide numerator and denominator by... check gcd.
Alternatively, due to symmetry and uniformity approximation, but exact computation confirms:
But better to write as reduced fraction. Verify:
Check if 20833 divides 62500? Unlikely. Check gcd:
But this is messy. Alternatively, accept symmetry: since the three dice are symmetric and the sum mod 3 is uniformly distributed under uniform independent choices? Not quite, because residue counts are not equal.