The "slow-speed collision" was reported just before 10 p.m. Friday near the south side of a terminal.
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According to the Los Angeles Fire Department, a tug driver was taken to a hospital in moderate condition, the bus driver and two passengers were transported in fair condition and the one person inside the plane, a worker, was treated, but declined to be taken to a hospital.
The plane was being towed from a gate to a parking area when it swiped the bus, the airport said.
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"We thank our partners @LAFD for quickly responding and treating passengers from the bus," LAX tweeted. "Other LAX operations remain normal."
A large skid mark from the plane's tire was visible, and the bus' windshield had extensive damage.