# import random library and set seed import random random.seed (123456)

# Step 1. # Define a function which randomly draws a ball with an integer between 1 and 100 on it; # then returns True if Player # wins and returns False if House wins. # Add a print statement to function to print random integer and test out function # Add comment statements to function # def drawball (n_plays) : ball = random.randint (1, 100) if (ball >=52): return True else : return False print (f' the number drawn is {ball}' ) drawball (1)

# Step 2. # Create a function which simulates playing the game n_plays times; keep track of number of wins and losses def gameplay (n_plays, funds, bet) : wins = 0 losses = 0 for i in range (0, n_plays) : if (drawball (n_plays) == True) : funds = funds +bet wins = wins + 1 else : funds = funds - bet losses = losses +1 return [funds, wins, losses] drawball (3)

#step 2 with a fake true and false #i tried printing out and tallying up wins to losses but it wasnt working with what i did above #i dont use this code for the remainder of the project but these are my thoughts on how to do that def draw (n_plays) : outcomes= ['true', 'false'] n_true = 0 ; n_false = 0 for i in range (0, n_plays) : ball = random.randint (1, 100) if (ball >= 52) : n_true = n_true +1 print ('true') else : n_false = n_false +1 print ('false') return ( [n_true, n_false]) draw (8)

print (gameplay (5, 10000, 100))

#simulation of 5 games x 100 total_funds = 0 total_wins = 0 total_losses = 0 results = [0, 0, 0] for i in range (1, 100) : results = gameplay(5, 10000, 100) total_funds = total_funds + results[0] total_wins = total_wins + results[1] total_losses = total_losses + results[2] averagefunds= total_funds / 100 print (f' the average number of funds after playing 5 games is {averagefunds}') #discrete probability calculations discprobwin= total_wins/500 discproblose= 1- discprobwin #complement rule applied discexpected= ((100*discprobwin) - (100*discproblose)) print (f' the discrete probability of winning is {discprobwin} and the discrete probability of losing is {discproblose}') print (f' the discrete expected value is {discexpected}')

#modification for losing about 2 dollars per game # in order to get a better approximation more games need to played according to the law of increasing numbers #number picked for amount of games is arbitrary; thats the biggest number i could input without the code taking too long to run results = gameplay(500000, 10000, 100) total_funds = results[0] total_wins = results[1] total_losses = results[2] discprobwin= total_wins/500000 discproblose= 1- discprobwin discexpected= ((100*discprobwin) - (100*discproblose)) print (f' the discrete probability of winning is {discprobwin} and the discrete probability of losing is {discproblose}') print (f' the discrete expected value is {discexpected}') #theoretical expected value is now closer to losing about 2 dollars per game whereas it was more than 8 dollars in the above section

# 1. import random and set seed import random random.seed (123456)

# 2. Input target sales and number of sales persons for upcoming year; low and high # percentages of sales for generating random numbers print ('***************************************') print ('sales rep 1') commission = actual sales * commission rate sales_low = 112500 ; sales_ high = 165000 sales1= random.randint (sales_low, sales_high) print ('the number of sales is', sales1)

# 3. Generate a random sales amount for each rep and check that it is in the correct range # Use a for loop; round answer to nearest cent

# 4. Add to your loop in # 3 to determine the commission for each rep # (you need an if-elif-else construct to determine rate); keep a running tab of # the sum of all commissions # round all dollar amounts to nearest cent #

# 5. Add a loop around your code in # 4 to do 10,000 simulations # Only print out the average commission for all 10,000 simulations # Don't print out all the information from Step # 4 - it will be way too much so remove # or comment out those print statements #