**The Birthday Paradox in Probability Theory****Overview:**The birthday paradox presents a probability scenario: what is the chance that in a group of \( n \) randomly selected people, at least two will share the same birthday?Many find it surprising, but in a room of 23 people, the probability of at least two of them sharing a birthday is about 50%! This counterintuitive fact is explained by the rapid increase in probability as the group size increases. In small classes at SBU, for example, the probability is nearly 100% for larger groups.**Experiment:**To understand this concept, we'll conduct a simple experiment. You'll complete the Python function `birthday_paradox`, which takes `num_students` as input—the number of students in a room. It generates `num_students` random integers between 1 and 365 (representing days of the year) and returns `False` if all values are unique or `True` if there is a duplicated value. The chance of a duplicate increases quickly as `num_students` rises.**Hint:**You can use the `set()` function in Python to find unique values in a list. For example:```pythonx = [1, 2, 3, 3]y = set(x) # y will be {1, 2, 3}```The length of this set can help you determine if there were duplicates in the original list.**Note:**Due to randomness, it’s hard to predict exact outcomes. The experiment involves running your function multiple times to get an average result for reliability.**Code Explanation:**```pythonimport randomdef birthday_paradox(num_students): return 0 # DELETE THIS LINE and start coding here. # Remember: end all your functions with a return statement, not a print statement!# Do not edit anything below this linedef birthday_trials(num_students, num_trials): same_birthday = 0 for i in range(num_trials): if birthday_paradox(num_students): same_birthday += 1 return same_birthday / num_trials# Test casesprint(birthday_trials(10, 10000)) # should be approx. 0.12print(birthday_trials(23, 10000)) # should be approx. 0.51print(birthday_trials(5, 10000)) # should be

The birthday paradox in probability theory asks what is the probability that in a set of n randomly chosen people, at least two of them share the same birthday. It is referred to as a paradox because many people wouldn't believe it when you hear the answer. In a room of 23 randomly chosen people, the probability that at least two of them share the same birthday is around 50%! Can you believe it? So even in smaller classes at SBU, the probability that at least two people share the same birthday is close to 100%! Instead of expecting you to simply accept this conclusion, we will be doing a little experiment to convince you that it's valid. Complete the function birthday_paradox, which takes one parameter, num_students, the number of students in a room. The function generates num_students random integers in the range [1, 365] and returns False if the values are all unique, or True if there is at least one duplicated value. As num_students increases, the likelihood that there is at least one duplicated value also increases, and rather quickly, at that! Hint: You can use the function set ( ) to take a list and create a copy that contains only the unique values. For example: x = [1, 2, 3, 3] y = set (x) Then y will be {1, 2, 3}. (The use of curly braces indicates that we have a set, a collection of unique values.) Consider what information you can glean (and what conclusions you can draw) by looking at the length of this new list. Note For experiments involving random values, it can be difficult to give examples of expected output. For this part, Colab will call your function many times to perform many simulations, and then report the average outcome. Your results may not exactly match the expected outcomes, but they should be "close". [ ] 1 import random 2 3 def birthday_paradox (num_students): 4 5 6 7 # Do not edit anything below this line 8 def birthday_trials (num_students, num_trials): 9 10 11 12 13 14 15 # Test cases # should be approx. 0.12 # should be approx. 0.51 16 print (birthday_trials (10, 10000)) 17 print (birthday_trials (23, 10000)) 18 print (birthday_trials(5, 10000)) # should be approx. 0.025 19 print (birthday_trials (100, 10000)) # should be approx. 1.0 20 return 0 # DELETE THIS LINE and start coding here. # Remember: end all of your functions with a return statement, not a print statement! same_birthday = 0 for i in range(num_trials): if birthday_paradox (num_students): same_birthday += 1 return same_birthday / num_trials