C3_W1_Lab 1_Four Birthday Problems

Course Q&A Math for Machine Learning Probability & Statistics for Machine Learning &...
1

In problem 1,
the solution to number of people needed such that probability of 2 people having same birthday comes out to be 254.

But in class the way it was solved it came out as 23.
What am I understanding incorrectly here?

1 Like
2

Kindly verify this. :face_with_peeking_eye:

Okay I think what I misunderstood is:

In the class-

We found that if we have 23 people then there is >50% chance that atleast 2 people have same birthday.
We tried finding probability that NO ONE has same birthday among themselves.

In lab problem 1-

The situation of interest is that NO ONE has birthday as that of one specific student. BUT there may be 2 people who have same birthday (just not same as the one specific student).
Ex. If bday of specific student is 1 March then no other student has birthday on 1 March BUT there maybe 2 students who have birthday of (say) 1 Jan.

1 Like
3

I also was somewhat confused by this, but but to make the lab problem_1 to match the lecture one would need to change it to problem_1_1

# before
def problem_1(n_students):
    
    # Predefine a specific birthday
    predef_bday = np.random.randint(0, 365)
    
    # Generate birthdays for every student
    gen_bdays = np.random.randint(0, 365, (n_students))
#     print(predef_bday in gen_bdays, predef_bday, gen_bdays)
    
    # Check if predefined bday is among students
    return predef_bday in gen_bdays
# after
def problem_1_1(n_students):
    
#  This is no longer relevant as we are looking at any two people and not one specific person
#     # Predefine a specific birthday
#     predef_bday = np.random.randint(0, 365)
    
    # Generate birthdays for every student
    gen_bdays = np.random.randint(0, 365, (n_students))
    # check if any two people have same birthday
    return len(gen_bdays) - len(np.unique(gen_bdays))