Old rule: An event can happen in two ways with probabilities P₁ and P₂. The probability of the event is then P₁ + P₂.
New rule: An event can happen in two indistinguishable ways with probability amplitudes A₁ and A₂. The probability of the event is then |A₁ + A₂|²

Old rule: An event can happen in two ways with probabilities P1 and P2. The probability of the event is then P1 + P2. New rule: An event can happen in two indistinguishable ways with probability amplitudes A1 and A2. The probability of the event is then |A1 + A2|2