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.
I do not see any short way of calculating this.
Are you meant to be writing a little computer program to do it?
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)
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.
Thanks for the input.
You have given good insight into a number of questions.
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