{}
# Online Python compiler (interpreter) to run Python online.
# Write Python 3 code in this online editor and run it.
import numpy as np
#The doors are numbered as 0,1,2.
#We will do N trials
N=100000
contestant_1_wins=0
contestant_2_wins=0
for _ in range(N):
#The door with the prize is chosen at random by the host
prize_door=np.random.randint(3)
#The contestant chooses a random door
chosen_door=np.random.randint(3)
#The host randomly picks a door which does not hide the prize and opens it
opened_door=np.random.choice([d for d in range(3) if d not in [chosen_door, prize_door]])
#The remaining door is losing.
losing_door=[d for d in range(3) if d not in [opened_door, prize_door]][0]
#The contestant switches doors
if(chosen_door==prize_door):
chosen_door=losing_door
else:
chosen_door=prize_door
# A new contestant enters the game, and choses randomly between the two doors.
new_contestant_door=np.random.choice([prize_door, losing_door])
# The prize door is revealed.
if(chosen_door==prize_door): contestant_1_wins+=1.
if(new_contestant_door==prize_door):contestant_2_wins+=1
print("Win probability for contestant 1: ", contestant_1_wins/N)
print("Win probability for contestant 2: ", contestant_2_wins/N)