### Instruction: If I roll 5 standard 6-sided dice and multiply the number on the face of each die, what is the probability that the result is a composite number?### Response: To find the probability of an event, I need to divide the number of favorable outcomes by the number of possible outcomes.
In this case, the possible outcomes are all the ways I can roll 5 dice, which is 6^5 = 7776.
The favorable outcomes are the ones where the product of the dice is a composite number, which means it has more than two factors.
One way to approach this is to count the number of unfavorable outcomes, where the product is a prime number or 1, and then subtract that from the total.
The only way the product can be 1 is if all the dice show 1, which is one outcome.
The only way the product can be a prime number is if one die shows a prime number and the rest show 1, which is 3 * 5 = 15 outcomes, since there are 3 prime numbers from 1 to 6 and 5 ways to choose which die shows the prime.
So the number of unfavorable outcomes is 1 + 15 = 16.
Therefore, the number of favorable outcomes is 7776 - 16 = 7760.
And the probability of getting a composite product is 7760 / 7776, which can be simplified by dividing both numerator and denominator by 16.
The simplified fraction is 485 / 486.