Write a function to calculate the expected number of empty boxes when you have 100 balls and 50 boxes, with each ball being placed into a random box independently. def expected_empty_boxes(balls: int, boxes: int) -> float: pass Inputs The inputs are defined as follows: balls: The number of balls to be distributed. Default should be 100. boxes: The number of boxes to distribute the balls into. Default should be 50. Output Return a float representing the expected number of empty boxes.

import random def simulate_empty_boxes(balls: int = 100, boxes: int = 50, iterations: int = 10000) -> float: total_empty_boxes = 0 # Run the simulation for the given number of iterations for _ in range(iterations): # Initialize a list to keep track of the number of balls in each box box_counts = [0] * boxes # Place each ball into a random box for _ in range(balls): random_box = random.randint(0, boxes - 1) box_counts[random_box] += 1 # Count the number of empty boxes in this iteration empty_boxes = box_counts.count(0) total_empty_boxes += empty_boxes # Calculate the average number of empty boxes across all iterations average_empty_boxes = total_empty_boxes / iterations return average_empty_boxes # Test the simulation function expected_empty_boxes_simulation = simulate_empty_boxes() print(f"Expected number of empty boxes (simulation): {expected_empty_boxes_simulation:.2f}")

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