eliza creates a 6 sided die by randomly choosing 6 integers between 1 and 7 inclusive to paint onto the sides of a blank cube. what is the probability that the faces of her die sum to 20.
We have for the six faces the sum of the integers 1 through 7, inclusive, except for the one missing value m, and that sum is given to be 24. Therefore, 24 = 1 + 2 + 3 + 4 + 5 + 6 + 7 – m = 28 – m. So, m = 4, and the six faces are 1, 2, 3, 5, 6, 7, of which four values (2, 3, 5, 7) are prime, making the probability of rolling a prime to be 2/3.
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I think you may have answered the wrong problem. In 2019 State Sprint Round, there is a problem like this "Eliza creates a custom 6-sided die by randomly choosing six distinct integers from 1 to 7, inclusive, to paint onto the sides of a blank cube. She tells Philip that the faces of her die have a sum of 24. Philip rolls the die. What is the probability that Philip’s die shows a prime number on the top face? Express your answer as a common fraction."
However, this seems to be a different version of the problem since the numbers don't have to be distinct.
Sadly, I wasn't able to answer your problem, however I was able to run a quick code in Python that gave me the answer.
The total number of possible combinations are 6891.
6891/117649 is our answer.
However, I'm not the most sure.
Sorry I wasn't able to help more.