#ChatGPT: Write a Python program which computes a random number in [0,1], 
#  and repeats this process #until a smaller value is computed.  
#  What is the average length of such a sequence?  Expected answer is 2.7.
#

import random

def generate_sequence():
    count = 1
    current_value = random.random()  # First random number in [0, 1]
    
    while True:
        next_value = random.random()  # Generate the next random number
        if next_value < current_value:
            break  # Stop if the next number is smaller than the current one
        current_value = next_value
        count += 1
    
    return count

def average_length(num_trials):
    total_length = 0
    for _ in range(num_trials):
        total_length += generate_sequence()
    return total_length / num_trials

# Run the simulation with 100,000 trials
num_trials = 100000
avg_len = average_length(num_trials)
print(f"Average length of the sequence: {avg_len}")