Being a hobbiest programmer, I know enough about probability to get by. However, I've set myself an impossible (for me) calculation in my current personal project.(adsbygoogle = window.adsbygoogle || []).push({});

I have a set of numbers. For this particular problem it is a set of four numbers {248, 184, 120, 56}, but I'll be repeating the process for many different sets of numbers (both in value and size).

Twice, I randomly draw a number from the set. Each draw is independent of the last so each draw can be thought of as a roll of 2 identical dice. I am looking for the following probabilities occuring:

(248.248) || (248.184) || (248.120) || (248.56) || (184.120) = 1998/2000

(184.184) || (184.56) || (56.56) = 1/2000

(120.120) || (120.56) || (56.56) = 1/2000

And wondering which way I should 'load' my dice i.e. how many sides do they need and on how many sides should each number appear?

I'm not sure of the notation mathematics uses for this, so I've stuck in logical operators as used in computing. "." = AND, "||" = OR. I guess I'm looking for this

(A AND A) OR (A AND B) OR (A AND C) OR (A AND D) OR (B AND C) = 1998/2000

(B AND B) OR (B AND D) OR (D AND D) = 1/2000

(C AND C) OR (C AND D) OR (D AND D) = 1/2000

I've gotten close, but that (D AND D) reappearing in both groups has me absolutely stumped.

I'm more interested in the method than the answer (if there is one) as I need to repeat this for 183 more steps of different set sizes, values and probabilities and I'm calculating/feeding it all into my program by hand.

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# Working out the sides on a die and the numerical ratio on the die

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