# 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

Algebra ->  Algebra  -> Probability-and-statistics -> 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      Log On

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 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 fractionFound 2 solutions by solver91311, checkley77:Answer by solver91311(16877)   (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(12569)   (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.