Rolling four standard dice, what is the probability that the product of the four results is even and divisible by 3?

Guest Sep 5, 2021

#1**0 **

133 ones [ 4 dice beginning with 1]

152 twos [4 dice beginning with 2 ]

189 threes[4 dice beginning with 3]

152 fours [4 dice beginning with 4]

133 fives [4 dice beginning with 5 ]

216 sixes [4 dice beginning with 6 ]

Total number of all possible permutations of the products of 4 dice that are all even and divisible by 3==** 133 + 152 + 189 + 152 + 133 + 216==975 The probability is: 975 / 6^4==325 / 432**

Guest Sep 5, 2021

#2**0 **

I decided to verify this with programming and found that my program gave the answer as 974. I didn't include details about distribution with that, but a little more poking around with it revealed that the program only found 188 instances of "threes" to your 189. I don't blame you for getting that wrong, counting is hard

helperid1839321
Sep 6, 2021