If we both arrive at the fountain at an independently random time between noon and 1, what are the chances our picnic actually happens?

170331_538riddler_lunchtime.py

# https://fivethirtyeight.com/features/what-are-the-chances-well-meet-for-lunch/

# On a lovely spring day, you and I agree to meet for a lunch picnic at the fountain in the center of our favorite park.
# We agree that we’ll each arrive sometime from noon and 1 p.m.,
# and that whoever arrives first will wait up to 15 minutes for the other.
# If the other person doesn’t show by then, the first person will abandon the plans and spend the day with a more punctual friend.
# If we both arrive at the fountain at an independently random time between noon and 1, what are the chances our picnic actually happens?

import random
# Seed makes the result identical for every run
# random.seed(1)

# 60 sided die
# 12:00 – 12:59
def d60():
    result = random.randint(0, 59)
    return result

wait_time = 15
# This is where we'll save the output
simluation_result = list()

# Simluation for lunch dates
def lunch_date(iterations):
    for x in range(iterations):
        # By default, no lunch happens
        lunchtime = 0
        # Person A at random time
        alex_arrives = d60()
        # Person B at random time
        beth_arrives = d60()
        # Did they arrive at the sametime?
        if alex_arrives == beth_arrives:
            # debug_times()
            # print('wow same time!')
            # print('Lunchtime!!!!!!')
            lunchtime = 1
        # Does Alex arrive first?
        elif alex_arrives < beth_arrives:
            # debug_times()
            if alex_arrives + wait_time >= beth_arrives:
                lunchtime = 1
            else:
                pass
        # If Alex didn't arrive first, logically Beth will have arrived first. 
        elif beth_arrives < alex_arrives:
            # debug_times()
            if beth_arrives + wait_time >= alex_arrives:
                lunchtime = 1
            else:
                pass

        simluation_result.append(lunchtime)

# What times did both people arrive?
def debug_times():
    print('Alex got here at', '12:', alex_arrives)
    print('Beth got here at', '12:', beth_arrives)

# 1 million iterations!
iterations = 1000000
# lunch_date(iterations)

for i in range(10):
    lunch_date(iterations)
    print(100 * simluation_result.count(1) / iterations)
    simluation_result = list()

Instead of count(1) you can use reduce.
In this case, they're equivalent. But if the list is like, [1, 3, 5, 2, 1, 99], then reduce would become the clearly correct choice.

EDIT: Python also has a built-in function called sum: http://stackoverflow.com/questions/13909052/how-do-i-add-together-integers-in-a-list-in-python