  It is commonly believed that our own Milky Way is on a collision course with
the neighbouring Andromeda galaxy. As a result of their merger, predicted in
around five billion years, the two large spiral galaxies that define the
present Local Group would form a new elliptical galaxy. Here we consider the
latest and most accurate observations by the Gaia and Hubble space telescopes,
along with recent consensus mass estimates to derive possible future scenarios
and identify the major sources of uncertainty in the evolution of the Local
Group over the next 10 billion years. We find that the next most massive Local
Group member galaxies -- namely, M33 and the Large Magellanic Cloud --
distinctly and radically affect the Milky Way - Andromeda orbit. While
including M33 increases the merger probability, the orbit of the Large
Magellanic Cloud runs perpendicular to the Milky Way - Andromeda orbit and
makes their merger less likely. In the full system, we find that uncertainties
in the present positions, motions, and masses of all galaxies leave room for
drastically different outcomes, and a probability of close to 50% that there is
no Milky Way - Andromeda merger during the next 10 billion years.
