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‎Tutorial4_Simulations_HosnaHamdieh.py‎

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# Tutorial 4: Simulations
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# Due: Tuesday, March 23 @ 11:55 PM
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# Hosna Hamdieh
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# A4: This assignment had 5 questions pluse an extra and in order to run each uncomment the function at the end of each
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############################ 1. Blood Pressure #########################
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# High blood pressure can require immediate medical attention. Write a program that allows a
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# doctor to identify a patient's blood pressure category given the systolic and diastolic blood
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# pressure.
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class Doctor:
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def __init__(self,Systolic_Blood_Pressure,Diastolic_Blood_Pressure):
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self.Systolic_Blood_Pressure=Systolic_Blood_Pressure
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self.Diastolic_Blood_Pressure=Diastolic_Blood_Pressure
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def Blood_Pressure_Category(self):
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if self.Systolic_Blood_Pressure<120 and self.Diastolic_Blood_Pressure<80:
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self.Category="Normal"
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elif self.Systolic_Blood_Pressure<129 and self.Diastolic_Blood_Pressure<80:
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self.Category = "Elevated"
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elif self.Systolic_Blood_Pressure<139 or self.Diastolic_Blood_Pressure<89:
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self.Category = "Hypertension Stage 1 "
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elif self.Systolic_Blood_Pressure<180 or self.Diastolic_Blood_Pressure<120:
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self.Category = "Hypertension Stage 2 "
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elif self.Systolic_Blood_Pressure>180 or self.Diastolic_Blood_Pressure>120:
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self.Category = "Hypertensive crisis "
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return self.Category
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def Blood_Pressure():
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print("Welcome")
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Systolic_Blood_Pressure = int(input("What is your Systolic_Blood_Pressure? "))
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Diastolic_Blood_Pressure = int(input("What is your Diastolic_Blood_Pressure "))
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BP=Doctor(Systolic_Blood_Pressure,Diastolic_Blood_Pressure)
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BPC = BP.Blood_Pressure_Category()
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print(f"Based on the information you have shared your blood pressure category is {BPC}")
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# Blood_Pressure()
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############################################## 2. Yahtzee ##############################
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# In the game of Yahtzee, players roll 5 dice, and score different points depending on the dice
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# they roll. A player rolls a “Yahtzee” when all 5 of the dice have the same value. Develop a Monte
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# Carlo simulation in Python to estimate the probability of rolling a Yahtzee.
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#roll the dice
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def roll():
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import random
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Values = []
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for i in range(0, 5):
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Value = random.randint(1,6)
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Values.append(Value)
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return Values
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# Yahtzee win
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def play():
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Values = roll()
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Game=""
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if Values[0]==Values[1]==Values[2]==Values[3]==Values[4]:
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Game = "win"
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print("You have won in Yahtzee")
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else:
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print("Maybe next time")
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return Game
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# Monte Carlo simulation of Yahtzee
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def Yahtzee():
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n=int(input("How many times do you want to run the simulation? "))
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win=0
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for i in range(n):
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Game = play()
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if Game == "win":
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win += 1
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probability_of_win = win/n
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print(f"Out of {n} times you have won {win} which means the probability of winning this game is {probability_of_win} which is not that high")
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#Yahtzee() # needs n
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# Some results
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# Yahtzee() # for n=100 => Out of 100 times you have won 1 which means the probability of winning this game is 0.01 which is not that high
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# Yahtzee() # for n=1000 => Out of 1000 times you have won 1 which means the probability of winning this game is 0.001 which is not that high
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# Yahtzee() # for n=10000=> Out of 10000 times you have won 6 which means the probability of winning this game is 0.0006 which is not that high
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# Yahtzee() # for n=100000 => Out of 100000 times you have won 75 which means the probability of winning this game is 0.00075 which is not that high
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# Yahtzee() # for n=1000000 => Out of 1000000 times you have won 777 which means the probability of winning this game is 0.000777 which is not that high
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###################################################### 3. Birthdays ####################
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# The birthday problem concerns the probability that within a group of n randomly selected
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# people, two people will have the same birthday. For example, in a group of 70 random people,
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# there is a 99.9% chance that two people will share the same birthday.
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# https://en.wikipedia.org/wiki/Birthday_problem
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# Develop a Monte Carlo simulation in Python to estimate the probability that in our class of 30
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# students, at least two students share a birthday.
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def Duplicate_Birthdays(n):
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global yes
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from random import randint
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BD=[]
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d=0
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for i in range(n):
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bd=randint(1,365)
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if bd not in BD:
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BD.append(bd)
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else:
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d+=1
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if d!=0:
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yes += 1
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probability_of_duplicates = d/n
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print(f"Out of {n} people in the room same birthdays happened {d} times")
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return d
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def Birthdays():
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m=int(input("How many times do you like to run the simulation: "))
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global yes
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yes=0
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n = int(input("How many people are in the class? "))
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D=0
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for i in range(m):
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d = Duplicate_Birthdays(n)
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D += d
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Pyes = yes/(m)
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# probability_of_duplicates=D/(m*n)
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print(f"The chances of at least two people having the same birthday in a room with {n} people after repeting the simulation {m} times is {Pyes} and in this run same birthdays happened {D} times")
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# Birthdays_Simulation() # inputs needed n,m
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# some results
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# Birthdays_Simulation() # for n=30,m=10000 => The chances of at least two people having the same birthday in a room with 30 people after repeting the simulation 10000 times is 0.7059 and in this run same birthdays happened 11523 times
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# Birthdays_Simulation() # for n=30,m=100000=> The chances of at least two people having the same birthday in a room with 30 people after repeting the simulation 100000 times is 0.70681 and in this run same birthdays happened 116114 times
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###################################################################### 4. Craps ############################
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# Craps is a dice game played at many casinos. A player rolls a pair of normal six-sided dice. If
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# the initial roll is 2, 3, or 12, the player loses. If the roll is 7 or 11, the player wins. Any other initial
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# roll causes the player to "roll for point." That is, the player keeps rolling the dice until either
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# rolling a 7 or re-rolling the value of the initial roll. If the player re-rolls the initial value before
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# rolling a 7, it's a win. Rolling a 7 first is a loss.
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# Write a program to simulate multiple games of craps and estimate the probability that the player
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# wins. For example, if the player wins 249 out of 500 games, then the estimated probability of
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# winning is 249/500 = 0.498.
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import random
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rng = range
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inp = input
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def makeNSidedDie(n):
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_ri = random.randint
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return lambda: _ri(1,n)
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class Craps_Play(object):
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def __init__(self):
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super(Craps_Play,self).__init__()
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self.die = makeNSidedDie(6)
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self.firstRes = (0, 0, self.lose, self.lose, 0, 0, 0, self.win, 0, 0, 0, self.win, self.lose)
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self.reset()
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def reset(self):
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self.wins = 0
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self.losses = 0
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def win(self):
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self.wins += 1
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return True
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def lose(self):
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self.losses += 1
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return False
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def roll(self):
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return self.die() + self.die()
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def play(self):
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first = self.roll()
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res = self.firstRes[first]
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if res:
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return res()
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else:
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while True:
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second = self.roll()
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if second == 7:
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return self.lose()
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elif second == first:
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return self.win()
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def times(self, n):
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wins = sum(self.play() for i in rng(n))
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return wins, n-wins
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def craps():
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import random
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c = Craps_Play()
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m = 0
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while True:
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try:
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n = int(input("How many rounds of craps would you like to play? (0 to quit) "))
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m += n
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print("Won {0}, lost {1}".format(*(c.times(n))))
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print("Based on the outcome the game probability of wining is {1} after {0} rounds""".format(n, (c.wins)/n))
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except:
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print("You have chosen to finish the game")
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break
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print("""In Total number of wins are {0}, and losses are {1}
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The probability of wining in total after playing the game {2} times is {3}""".format(c.wins, c.losses, m, (c.wins)/m))
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#craps()
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# Result
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"""How many rounds of craps would you like to play? (0 to quit) 10
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Won 5, lost 5
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Based on the outcome the game probability of wining is 0.5 after 10 rounds
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How many rounds of craps would you like to play? (0 to quit) 100
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Won 43, lost 57
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Based on the outcome the game probability of wining is 0.48 after 100 rounds
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How many rounds of craps would you like to play? (0 to quit) 1000
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Won 505, lost 495
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Based on the outcome the game probability of wining is 0.553 after 1000 rounds
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How many rounds of craps would you like to play? (0 to quit)
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You have chosen to finish the game
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In Total number of wins are 553, and losses are 557
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The probability of wining in total after playing the game 1110 times is 0.4981981981981982"""
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########################################################## 5. Gaming ######################
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# In a computer-based trading card game, players use in-game currency to draw cards. The
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# probability of drawing each card type is as follows:
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# Common: 94.3%
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# Rare: 5.1%
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# Legendary: 0.6%
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# However, because the rates for rare and legendary cards are so low, the game also includes the
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# following rules:
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# 1. If a Rare card is not drawn after 9 attempts, a Rare card is guaranteed on the 10th
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# attempt.
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# 2. If a Legendary card is not drawn after 75 attempts, the probability of drawing a
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# Legendary card on subsequent attempts increases to 30%.
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# 3. If a Legendary card is not drawn after 89 attempts, a Legendary card is guaranteed on
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# the 90th attempt.
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# Develop a Monte Carlo simulation to estimate the effective probabilities of drawing Rare and
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# Legendary cards.
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import random
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def drawCard(pc,pr,pl):
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r = random.random()
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if r < (pc/100):
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card = 'Common'
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elif r < (pc+pr)/100:
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card = "Rare"
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elif r >= (1-pl)/100:
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card = "Legendary"
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return card
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def Gaming():
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# testing
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A = int(input("""Which one would you like: 1. Testing with the probabilities avaiable in the program or test it with the numbers you want?
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Answer (1 or 2): """))
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if A == 1:
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pc, pr, pl = 94.3, 5.1, 0.6
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elif A == 2:
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pc = int(input("What is the probability of getting a common card? pc= "))
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pr = int(input("What is the probability of getting a rare card? pr= "))
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pl = int(input("What is the probability of getting a legendary card? pl= "))
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else:
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print("Your input is not valid")
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cards = []
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rare = 0
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legendary = 0
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common = 0
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i = 1
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P = (input("How many times do you want to simulate the card function: "))
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try:
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play = int(P)
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for i in range(play):
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# If a Legendary card is not drawn after 89 attempts, a Legendary card is guaranteed on the 90th attempt.
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if "Legendary" not in cards[-89:]:
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card = "Legendary"
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# If a Rare card is not drawn after 9 attempts, a Rare card is guaranteed on the 10th attempt.
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elif "Rare" not in cards[-9:]:
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card = "Rare"
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# If a Legendary card is not drawn after 75 attempts, the probability of drawing a Legendary card on subsequent attempts increases to 30%.
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elif "Legendary" not in cards[-75:]:
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pcn = pc - (30 - pl)
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pln = 30
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card = drawCard(pcn, pr, pln)
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else:
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card = drawCard(pc, pr, pl)
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cards.append(card)
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if card == 'Common':
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common += 1
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elif card == "Rare":
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rare += 1
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else:
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legendary += 1
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# play = input(
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# f"""You have randomly selected {i} cards up to now enter if you do not want to continue otherwise type more """)
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i += 1
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# Probabilities after doing the simulation
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print(f"""You have randomly selected {i} cards and the list of cards is {cards}
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The total number of common cards is {common}, rare cards is {rare}, and you got {legendary} legendary cards
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Based on the simulation the probabilities are:
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The probability of getting a common card is {common/play},
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The probability of getting a rare card is {rare/play},
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The probability of getting a legendary card is {legendary/play}
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We can see that new roles have increased the probability of getting rare cards and legendary cards a bit""")
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except:
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print("Your input is not valid")
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#Gaming() # the number of sumilation is needed there is also a chance of changing the probabilities
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"""outcome after trying the simulation for n=1000 is:
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You have randomly selected 1000 cards
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The total number of common cards is 861, rare cards is 124, and you got 15 legendary cards
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Based on the simulation the probabilities are:
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The probability of getting a common card is 0.861,
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The probability of getting a rare card is 0.124,
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The probability of getting a legendary card is 0.015
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We can see that new roles have increased the probability of getting rare cards and legendary cards a bit"""
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"""outcome after trying the simulation for n=100 is:
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The total number of common cards is 84, rare cards is 13, and you got 3 legendary cards
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Based on the simulation the probabilities are:
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The probability of getting a common card is 0.84,
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The probability of getting a rare card is 0.13,
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The probability of getting a legendary card is 0.03
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We can see that new roles have increased the probability of getting rare cards and legendary cards a bit"""
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########################################## Bonus ####################################
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"""An E. coli bacterium is swimming in a porous circular bag with a radius of 1 mm. Every second,
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the bacterium randomly changes the direction that it is swimming in. If the bacterium starts in
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the centre of the bag, and swims at a rate of 0.06 mm per second, how long, on average, will it
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take the bacterium to escape the bag? """
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"""To make things visible the scales were change and multiplied by 50 that is why the speed was changed from 0.06 to 3 and similarly to make things go faster the time step was changed from 1 second to 0.001 but each step is counted and the time is calculated based on each movement happening in one second.
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One problem was that the bag size had to be converted and it was not obvious at first.
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"""
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from math import *
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import graphics
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from random import *
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import time
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def Brownian_Motion():
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win = graphics.GraphWin("Brownian", 500, 500)
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p0 = graphics.Point(250, 250)
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# converting the bage size based on the fact that each pixel is 26 mm in each side
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# making dimentions bigger to be visiable so all sizes are multiplied by 50
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bag = graphics.Circle(p0, 5000/(26*(2**0.5)))
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bag.setFill("lightsteelblue")
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bag.draw(win)
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particle = graphics.Circle(p0, 10)
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particle.setFill("yellow")
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particle.draw(win)
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i = 1
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x = [500]
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y = [500]
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while win.checkMouse() == None:
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# making the simulations faster by 1000 times
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time.sleep(0.001)
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p = particle.getCenter()
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angle = random() * 2 * pi
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x.append(x[i-1] + cos(angle))
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y.append(y[i-1] + sin(angle))
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#line = graphics.Line(p, p0).draw(win)
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d = (((((x[i] - x[0])/50) ** 2) + (((y[i] - y[0])/50) ** 2)) ** 0.5)
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if d <= 1:
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particle.move(sin(angle) * 0.06*50, cos(angle) * 0.06*50)
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pn = particle.getCenter()
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line = graphics.Line(p, pn).draw(win)
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print(f"the new point is located in x={x[i]} and y={y[i]} and is {d} far from the start point")
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# since each step should have been 1 second we can assume that the number of times we repeat it would be the time taken in seconds
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i += 1
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else:
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print(f"It took {i} seconds for the Brownian to reach the bag's border and go out of it")
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break
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win.getMouse()
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win.close()
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return i
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def Bonous():
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n = int(input("How many times do you want to simulate this function: "))
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Ttime = 0
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Times = []
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for i in range(n):
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t = Brownian_Motion()
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Times.append(t)
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Ttime += t
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ta = Ttime/n
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print(f"""After repeating the process {n} times the average time of scape is {ta}
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List of scape times is: {Times}""")
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Bonous() # number of symulation is needed
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"""
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It took 6925 seconds for the Brownian to reach the bag's border and go out of it
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It took 2121 seconds for the Brownian to reach the bag's border and go out of it
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It took 5222 seconds for the Brownian to reach the bag's border and go out of it
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It took 3062 seconds for the Brownian to reach the bag's border and go out of it
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It took 1106 seconds for the Brownian to reach the bag's border and go out of it
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After repeating the process 5 times the average time of scape is 3687.2"""
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"""After repeating the process 10 times the average time of scape is 1907.0
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List of scape times is: [4283, 2568, 1651, 504, 2335, 1537, 1099, 2957, 1565, 571]"""
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############################################## The End ##################################

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