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5 dice will be thrown one by one, then the product of the 5 numbers will be counted. Which will be higher, the product probability of 180 or the product probability of 144?

 Jan 7, 2020
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This is my attempt at this one:

 

180 = 2 x 2 x 3 x 3 x 5 =15 - This is the sum of the prime factors of 180.

This one has : 5! /2!2! =30 permutations

So, 30 / 120 = 1/4 = 25 % probability 

 

144 =4 x 2 x 2 x 3 x 3 = 14 - This is  one of the the sums of the prime factors of 144.

144 =2 x 2 x 2 x 3 x 6 = 15 - This is the other possible sum of the prime factors of 144.

The first one has : 5! / 2!2! = 30 permutations

The 2nd one has :  5! / 3!    = 20 permutations

And this one has : [30 + 20] /120 =41.667% probability

 

 

Therefore, the product probability of 144 > 180.

 

P. S. For goodness sake, some mathematician should check this !!! Thanks. 

 Jan 7, 2020
edited by Guest  Jan 7, 2020
edited by Guest  Jan 7, 2020

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