import numpy as np

def sigmoid(z):
    return 1 / (1 + np.exp(-z))


def logistic_regression_predict(x, w, b):
    z = w * x + b
    return sigmoid(z)


distances = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype=float)
late = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], dtype=float)

w, b = 2, -11
probabilities = logistic_regression_predict(distances, w, b)

for d, p, actual in zip(distances, probabilities, late):
    print(f"{d:.0f} km -> P(late) = {p:.4f}  (actually {'late' if actual else 'not late'})")

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