import numpy as np
import numpy.random as rd
import matplotlib.pyplot as plt
import numpy.linalg as lin

# 1)
def ecart(a,b):
    V=lin.eigvals(np.array([[3*a-2*b,-6*a+6*b+3],[a-b,1-2*a+3*b]]))
    return int(100*abs(V[0]-V[1]))/100
# 2)
def hasard(p):
    A=rd.geometric(p,500)
    B=rd.geometric(p,500)
    c=0
    for k in range(500):
        if ecart(A[k],B[k])>=0.1:
            c=c+1
    return c

X=np.arange(0.01,1,0.01)
Y=[hasard(x)/500 for x in X]
plt.plot(X,Y)
plt.show()

Z=[(2-2*x+x*x)/(2-x) for x in X]
plt.plot(X,Y,X,Z)
plt.show()