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def binom(x, y):
    try:
        binom = fac(x) // fac(y) // fac(x - y)
    except ValueError:
        binom = 0
    return binom


###This function takes inputs and outputs the probability
#of success in one trial
#pcalc is short for probability calculation
def pcalc(masternodes,quorumsize,attacksuccess,Byznodes):
    SampleSpace = binom(masternodes,quorumsize)
    pctemp=0
    for x in range(attacksuccess, quorumsize+1):
        pctemp = pctemp + binom(Byznodes,x)*binom(masternodes-Byznodes,quorumsize-x)
    #at this juncture the answer is pctemp/SampleSpace
    #but that will produce an overflow error.  We use logarithms to
    #calculate this value
    return 10 ** (log(pctemp,10)- log(SampleSpace,10))