If one light bulb burns out in a string of lights, and the rest stay lit, it is reasonable to assume that the lights are wired in

The lights are wired in PARALLEL.

In fact, when the lights are connected in parallel, they are connected on separate branches to the source of voltage, so if one light bulb burns out, the other lights continue to work because the current continues to flow in the other branches of the circuit.

Vice-versa, if the light bulbs are connected in series, they are on the same branch This means that if one of them burns out, the circuit is open in that point, so the current cannot flow anymore and the other light bulbs turn off as well.