from typing import List
import random


def random_state(width: int, height: int) -> List[List[int]]:
    """Generates a board with all the cells randomly dead (0) or alive (1).

    Args:
        width: The width of the board to be created.
        height: The height of the board to be created.

    Returns:
        A list of lists representing the board in a 2D space.
    """
    return [[int(random.random() * 2) for _ in range(width)] for _ in range(height)]