Question

python. It is better to use "random"

Now we want to analyze how often the tortoise and hare win or lose the race as we vary the race length. We can wrap the logic of our race simulation in a function and then call it many times to simulate many races. Then, we can collect some statistics to see how likely is it that the tortoise (or hare) wins a race of a given length. Specifically, write a function simulate_race that takes one argument, race_length, which is a positive integer that gives the length of the race (so, 100 is no longer-hard coded as the race's length). The function returns one of three strings: 'tortoise', 'hare' or 'tie', to indicate which animal won the race or whether there was a tie. Outside your simulate_race function, in a loop, call your method exactly 10000 times with varying race lengths as indicated in the table of experiments below and compute the winning percentages of the tortoise and hare, and also the percentage of times that they tie. What you will find is that the percentages vary as the race length changes. Below is the algorithm you should implement for running the experiments: initialization of variables to compute statistics for i in range (10000): call simulate_race(N) # where N is 50, 100, 250 or 1000 for this experiment update statistics variables as needed print winning % for tortoise and hare (separately), and % ties for this experiment Expected Results (all percentages are approximate): Experiment % Tortoise Wins % Hare Wins % Ties 10,000 calls of simulate_race (50) 63% 3% 34% 10,000 calls of simulate_race(100) 70% 2% 28% 79% 1% 20% 10,000 calls of simulate_race (250) 10,000 calls of simulate_race (1000) 95% 0% 5% Slow and steady really does win the race, especially if it's a long race!

Answer 1

Q1:

Sol:

# program in Python to simulate biased winner

import random # for random function
# number of experiments done
race_length = [50,100,250,1000]
# array to hold the outcomes
# note that we have designed this array to have biased results on tortoise
arr = ["tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise", "tortoise", "tortoise","tortoise", "tortoise", "tortoise", "tortoise", "tortoise", "tortoise", "tortoise", "tortoise", "tortoise","hare","tie","tie","tie","tie"]
# function to simulate race
def simulate_race(num):
# returns the biased results based on race_length
return arr[random.randint(round((1000-num)/45),34)]
# print the table header
print("-------------------------------------------------------")
print("Experiment | % Tortoise Wins | % Hare Wins | % Ties\n")
print("-------------------------------------------------------")
for length in race_length:
# variables for winners
hareWin = 0;
tortWin = 0;
tie = 0;
# loop 10000 times for simulation
for i in range(10000):
winner = simulate_race(length)
# find the winner and update respective variables
if winner == "hare":
hareWin = hareWin + 1
elif winner == "tortoise":
tortWin = tortWin + 1
else:
tie = tie + 1;
# print the results row wise
print(length , "\t | " , str(round(tortWin*0.01)) , "%\t | " , str(round(hareWin*0.01)) , "%\t | " , str(round(tie*0.01)), "%\n")

# Output

-------------------------------------------------------
Experiment | % Tortoise Wins | % Hare Wins | % Ties

-------------------------------------------------------
50             |  65 %      |  7 %        |  28 %

100        |  67 %          |  6 %        |  27 %

250        |  73 %          |  5 %        |  22 %

1000       |  86 %          |  3 %        |  11 %

# Screenshot of Code (for reference to indentation)

main.py 1 # program in Python to simulate biased winner 2 3 import random # for random function 4 # number of experiments done 5 race_length = [50,100,250,1000] 6 # array to hold the outcomes 7 # note that we have designed this array to have biased results on tortoise 8 arr = ["tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise", 9 "tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise","tortoise", "tortoise", "tortoise","tortoise", "tortoise", "tortoise", 10 "tortoise", "tortoise", "tortoise", "tortoise", "tortoise", "tortoise","hare","tie","tie","tie","tie"] 11 # function to simulate race 12 - def simulate_race(num): 13 # returns the biased results based on race_length 14 return arr[random.randint(round((1000-num)/45), 34)] 15 # print the table header 16 print("---- -") 17 print("Experiment | % Tortoise Wins | % Hare Wins | % Ties\n") 18 print(" --") 19. for length in race_length: 20 # variables for winners 21 harewin = 0; 22 tortwin = 0; 23 tie = 0; 24 # loop 10000 times for simulation 25 for i in range(10000): 26 winner = simulate_race(length) 27 # find the winner and update respective variables 28 - if winner == "hare": 29 harewin = hareWin + 1 30 elif winner == "tortoise" : 31 tortwin = tortWin + 1 32 else: 33 tie = tie + 1; 34 # print the results row wise 35 print(length, "\t | " , str(round(tortwin*0.01)), "At |", str(round(hareWin*0.01)), "%\ | ", str(round(tie*0.01)), "%\n") 36

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