SOLUTION: Four standard six-sided dice are rolled. What is the probability that the product of the numbers on the top faces of all four dice is a prime number? Express your answer as a commo

Question 218462: Four standard six-sided dice are rolled. What is the probability that the product of the numbers on the top faces of all four dice is a prime number? Express your answer as a common fraction
Found 2 solutions by solver91311, checkley77:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are different results for rolling 4 six-sided dice. The only way the product of the four upper faces can be prime is if three of the upper faces show a 1 and the remaining upper face shows a prime number less than 6, namely 2, 3, or 5. Here are the possibilities

1, 1, 1, 2
1, 1, 1, 3
1, 1, 1, 5
1, 1, 2, 1
1, 1, 3, 1
1, 1, 5, 1
1, 2, 1, 1
1, 3, 1, 1
1, 5, 1, 1
2, 1, 1, 1
3, 1, 1, 1
5, 1, 1, 1

for 12 possible successful outcomes.

John

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Prime products:
1*1*1*1=1
1*1*1*3=3
1*1*1*5=5
1*1*3*1=3
1*1*5*1=5
1*3*1*1=3
1*5*1*1=5
3*1*1*1=3
5*1*1*1=5
Probability = (number of successes)/(total outcomes).
9/6^4=9/1,296=1/144 ans.
A sample space diagram could also be used here but I don't have much success in creating one.

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