from math import sqrt
def factorielle(n):
    if n==0:
        return 1
    else:
        return n*factorielle(n-1)
def C(n,k):
    return factorielle(n)//(factorielle(k)*factorielle(n-k))
def binomFdp(n,p,k):
    return C(n,k)*p**k*(1-p)**(n-k)

def BT(n,p):
    return sum(binomFdp(n,p,k) for k in range(n+1) if abs(k-n*p)>sqrt(n)),p*(1-p)