# Define ranges for each parameter in the Drake equation
R_star = 1 # Rate of star formation in the Milky Way (stars per year)
f_p = np.random.uniform(0.7, 1.0, 100000) # Fraction of stars with planets
n_e = np.random.uniform(0.1, 0.2, 100000) # Number of potentially habitable planets per system
f_l = np.random.uniform(1e-5, 1.0, 100000) # Fraction where life emerges
f_i = np.random.uniform(1e-5, 1.0, 100000) # Fraction where intelligence evolves
f_c = np.random.uniform(0.01, 1.0, 100000) # Fraction of detectable civilizations
L = np.random.uniform(100, 1e6, 100000) # Duration of detectability (years)

# Calculate the number of civilizations in the galaxy for each simulation
N = R_star * f_p * n_e * f_l * f_i * f_c * L

# Calculate the probability that N < 1 (we are alone)
prob_alone = np.sum(N < 1) / len(N)
median_civilizations = np.median(N) # Median number of civilizations

prob_alone, median_civilizations