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119 lines (84 loc) · 1.91 KB
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##############################
# Probablité - Paradoxe de Parrondo
##############################
# Référence : "Paradoxe de Parrondo", La gazette des mathématiciens, juillet 2017
from random import *
##############################
# Activité 1 - Jeu A : premier jeu perdant
##############################
## Question 1 ##
def tirage_jeu_A():
x = random()
if x <= 0.49:
return +1
else:
return -1
## Question 2 ##
def gain_jeu_A(N):
gain = 0
for i in range(N):
gain = gain + tirage_jeu_A()
return gain
## Question 3 ##
def esperance_jeu_A(N):
esperance = gain_jeu_A(N)/N
return esperance
# Test
print("--- Jeu A ---")
N = 1000000
print(esperance_jeu_A(N))
##############################
# Activité 2 - Jeu B : premier jeu perdant
##############################
## Question 1 ##
def tirage_jeu_B(g):
if g%3 == 0:
x = random()
if x <= 0.09:
return +1
else:
return -1
else:
x = random()
if x <= 0.74:
return +1
else:
return -1
## Question 2 ##
def gain_jeu_B(N):
gain = 0
for i in range(N):
gain = gain + tirage_jeu_B(gain)
return gain
## Question 3 ##
def esperance_jeu_B(N):
esperance = gain_jeu_B(N)/N
return esperance
# Test
print("--- Jeu B ---")
N = 1000000
print(esperance_jeu_B(N))
##############################
# Activité 3 - Paradoxe de Parrondo
##############################
## Question 1 ##
def tirage_jeu_AB(g):
x = random()
if x < 0.5:
return tirage_jeu_A()
else:
return tirage_jeu_B(g)
## Question 2 ##
def gain_jeu_AB(N):
gain = 0
for i in range(N):
gain = gain + tirage_jeu_AB(gain)
return gain
## Question 3 ##
def esperance_jeu_AB(N):
esperance = gain_jeu_AB(N)/N
return esperance
# Test
print("--- Jeu AB ---")
N = 1000000
print(esperance_jeu_AB(N))