4 10 points The birthday problem is as follows given a group

4. (10 points The birthday problem is as follows: given a group of n people in a room, what is the probability that two or more of them have the same birthday? It is possible to determine the answer to this question via simulation. Write a function called calcBirthdayProbability that takes as input n and calculates the probability that two or more of the n people will have the same birthday. To do this, the function should create an array of size n and generate n birthdays in the range 1 to 365 randomly. It should then check to see if any of the n birthdays are identical The function should perform this experiment 106 times and calculate the fraction of time during which two or more people had the same birthday The function is called as follows: probability calcBirthday Probability (numPeople) Examples of correct function behavior follow num People 10 prob calc Birthday Probability (numPeople) prob num People 20 prob calcBirthday Probability (numPeople) prob 0.4117 prob calcBirthday Probability (numPeople) prob 0.4114 prob calcBirthday Probability (numPeople) prob 0.4113 Note that different runs of the program with the same value for numPeople yield slightly different probability results. This is expected since we are performing experiments with randomly generated values during each run of the program. The Cody tests will be designed to account for this type of variation in the results

Solution

import random

def has_duplicates(listToCheck):
number_set = set(listToCheck)

if len(number_set) is not len(listToCheck):
return True
else:
return False

def calcBirthdayProbability(numPeople):
duplicateNumber=0
for i in range(0,1000):
birthdayList=[]

for j in range(0,numPeople):
birthday=random.randint(1,365)
birthdayList.append(birthday)

x = has_duplicates(birthdayList)

if x==True:
duplicateNumber+=1
print \"prob\ \"

print round(((duplicateNumber/1000.0)),3)

numPeople=input(\"Enter numPeople\ \")

calcBirthdayProbability(numPeople)

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Output:

akshay@akshay-Inspiron-3537:~/Chegg$ python birtday.py
Enter numPeople
20
prob

0.414

Each time probablity little bit changes due to random birthday dates