Python 3.3: Birthday Probability

Question

Trying to do the Birthday Program in python. Being a beginner in Python, I am having some trouble.

1. Function duplicates(l) that takes a list l and returns True if it has a duplicate element, and False if it does not.
2. Function test(count) generates a list of count random integers between 1 and 365 . Function duplicates(l) will test for duplicates.
3. Function probability(count, num) runs num tests of count people, and counts the number of tests with duplicates. It returns the fraction of the tests with duplicates - the number of duplicates divided by num.

results should look like:

For 2 people, the probability of 2 birthdays is 0.002.

For 3 people, the probability of 2 birthdays is 0.008. and so on...

---

Stuck on step 2 & 3:

import random

# not sure what to put for count
count = [random.randint(1, 365)]

def duplicates(l):
    if len(l)!=len(set(l)):
        return True
    else:
        return False

def test(count):
    return [random.randint(1, 365)]

#def probability(count,num):

I believe I did step one correctly, but I'm not sure where to go from here.

Answer 1

You should create the list like this. test isn't a very useful name. Consider something like make_birthday_list instead

def test(count):
    return [random.randint(1, 365) for x in range(count)]

The test in duplicates already evaluates to a bool, so you can just do this. It's not a good idea to use l as a variable name (looks too much like 1) so I changed it to the_list

def duplicates(the_list):
    return len(the_list)!=len(set(the_list))

You'll have to run the test over and over to get the probability

eg.

num_samples = 10000
for count in range(100):
    dup = 0
    for test_number in range(num_samples):
        the_list = make_birthday_list(count)
        if duplicates(the_list):
            dup += 1
    print(count, dup/num_samples)   # / returns a float in Python3

Answer 2

test does not return a list of length count. The result only has one element. You would want to make use of list comprehension to get this to work nice:

[random.randint(1, 365) for x in range(count)]

Then for step 3:

def probability(count,num):
    dup_trues = sum([duplicates(test(count)) for i in range(num)])  #***
    dup_falses = num-dup_trues
    return float(fails)/num

The host important line in the above function is labeled #*** Here's a breakdown of how it works:

The stuff in the square brackets is a list comprehension.

for i in range(num) says do this stuff with i=0, i=1, ...i=num-1. You know what duplicates and test does. So the list ends up with a bunch of trues and falses (ones and zeros)

sum adds up the elements of the list. So this gives us the number of trues

The next line dup_falses = num-dup_trues says we have num results altogether, those that aren't true are false.

return float(fails)/num the float is not necessary in python 3