Would a plane take off with only one passenger?

Almost always. The plane is needed in its destination for its next flight. Also the flight crew need to be at the destination.

As the flight date approaches, if the plane is under booked, the cost of seats can drop. Not too far. The airline doesn’t want a (normally) full fare paying passenger switching to your flight because it’s half the cost.

Most likely, for a variety of reasons:

  1. They still have a contractual obligation to get the passenger to their destination, so cancelling the flight means arranging (and paying for) alternative transportation which isn’t always easy or cheap at the last minute.
  2. The plane is likely also carrying cargo which they still need to transport.
  3. The plane and crew have a schedule to keep, just because the current flight is empty doesn’t mean their next scheduled flight will be, so they still need to make it to their destination to be ready for their next scheduled flight (or whatever else that may be next on their schedule e.g. maintenance for the plane, taking crew home, etc.).
  4. Leaving a plane on the ground also cost them money (airports don’t let them park for free).

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