In this exercise you will simulate 1,000 rolls of two dice. Begin by writing a function that simulates rolling a pair of six-sided dice. Your function will not take any parameters. It will return the total that was rolled on two dice as its only result.
Write a main program that uses your function to simulate rolling two six-sided dice 1,000 times. As your program runs, it should count the number of times that each total occurs. Then it should display a table that summarizes this data. Express the frequency for each total as a percentage of the total number of rolls. Your program should also display the percentage expected by probability theory for each total. Sample output is shown below.
| Total | Simulated % | Expected % |
|---|---|---|
| 2 | 2.90 | 2.68 |
| 3 | 6.90 | 5.56 |
| 4 | 9.40 | 8.33 |
| 5 | 11.90 | 11.11 |
| 6 | 14.20 | 13.89 |
| 7 | 14.20 | 16.67 |
| 8 | 15.00 | 13.89 |
| 9 | 10.50 | 11.11 |
| 10 | 7.90 | 8.33 |
| 11 | 4.50 | 5.56 |
| 12 | 2.60 | 2.78 |
Hint:
To simulate dice rolls first import random to your module. Then you can simulate the roll by using the code
r = random.randrange(6) +1
The reason we use +1 is that randrange will give us a random number from 0 and up to but not including the number we pass to it.
import random
def two_dice_roll():
dice1 = random.randrange(6) +1
dice2 = random.randrange(6) +1
return dice1 + dice2
def main():
#Create a dictionary for the results and set all values to 0
result_dict = {2:0, 3:0, 4:0, 5:0, 6:0, 7:0, 8:0, 9:0, 10:0, 11:0, 12:0}
#Simulate 1000 rolls and store the result
for turn in range(1000):
result = two_dice_roll()
#Add one to the dict using result as the key and by increasing its value by one
result_dict[result] += 1
#Now present the result
#First the title row.We use the rjust method on the strings to right adjust
#the text
print("Total".rjust(16),"|", "Simulated %".rjust(16),"|", "Expected %".rjust(16))
print("-------------------------------------------------------")
#Now print the results
for n in range(2,13):
#Calculate the simulated result and format it with 2 decimal
#places and convert it to a string
sim_result = str("%.2f"%(result_dict[n]/1000*100))
#To calculate the expected result we need to consider
#That the result of 7 is the most probable one
if n <= 7:
exp_result = str("%.2f"%((n-1)/36*100))
else: #so if n is greater than 7 we need to reduce the probability
exp_result = str("%.2f"%((12-n+1)/36*100))
#Now print this row using rjust method
print(str(n).rjust(16),"|",sim_result.rjust(16),"|",exp_result.rjust(16))
if __name__ == '__main__':
main()