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# Dice probability

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What is the probability of getting a sum that is a Prime Number between 17 and 37 (17, 19, 23, 29, 31, 37) on a roll of 7 fair 6-sided dice? Thank you for help.

Jan 17, 2020

#1
+110279
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I do not see any short way of calculating this.

Are you meant to be writing a little computer program to do it?

Jan 17, 2020
#2
+30689
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A brute force and ignorance program gives the following results:

17   there are 6538 ways

19   there are 12117 ways

23   there are 22967 ways

29   there are 15267 ways

31   there are 9142 ways

37   there are 462 ways

total = 66493 ways

Hence probability = 66493/67   (or  0.2375 approximately)

Jan 17, 2020
#3
+1

Hi Melody: Your question to the poster is spot on! I think this question is meant as computer coding assignment. There is, however, a specific formula, from Mathworld, that is formulated just for this kind of problem and it comes from this link: http://mathworld.wolfram.com/Dice.html [Equation 10]. We can use it to calculate the totals of 6 primes in question and sum them up. Here is the formula in question:                S=17; N=7; sumfor(k, 0, ((S - N)/6), ((-1)^k * (N nCr k) * (S - 6*k - 1) nCr (N - 1))

Alan: I'm even more ignorant as to how this formula was derived in the first place, to specifically compute dice sums!!.

17 = 6,538, 19 =12,117, 23 =22,967, 29 =15,267, 31 =9,142, 37 = 462.
GRAND TOTAL =6,538 + 12,117 + 22,967 +15,267 + 9,142 + 462 =  66,493 / 6^7 = 23.75 % probability of getting a prime number.

Jan 17, 2020
#4
+110279
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Hi Guest,

Thanks for the input.

You have given good insight into a number of questions.

It would be really good if you became a member, it is easy and free and i do not believe you will get more junk mail or any other 'nasties' as a consequence.

I would like to know when you are answering, be able to find you older  answers, and get to know you.  If you were a member I would be able to do much of this through your member page.

If you really do not want to join then please sign your contributions so that they are fully recognisable.  It will be nowhere near as good as being in your member name though.

Melody  Jan 18, 2020