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(17BII) Binomial Probability Distribution - Printable Version

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(17BII) Binomial Probability Distribution - Dave Britten - 05-28-2015 03:08 PM

Dieter and I had been discussing improving this algorithm here, and I realized it would be easy to implement on the 17BII solver with definite loops and iterative computation/summation. So here we are. Line breaks and C-like comments added for legibility.

Find the probability of rolling a six at least 40 times when rolling a standard six-sided die 120 times.

120 N
6 1/x P1
40 L
120 H

6.41962987692E-6, or .000642% (i.e. don't wager any money on that bet)

    0*(N+P1+L+H) //Set up menu variable ordering
    +0*L(B:N) //Initialize B
    +0*Σ(X:2:L:1: //Iteratively compute B=nCr(N,L)
    +0*L(PΣ:L(B:G(B)*P1^L*(1-P1)^(N-L))) //Initialize PΣ with BinProb(N,L,P)
    +0*Σ(X:L:H-1:1: //Iteratively compute sum of BinProb(N,L..H,P)
    +PΣ=PΣ //Spit out result