The accident occurred at the intersection of Cedar and Alluvial.
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According to Fresno Police, the bus driver was traveling southbound on Cedar when he was distracted by talking to a passenger and ran a red light.
The bus and the SUV then pushed into three other vehicles that were in the left lane getting ready to turn left on Alluvial.
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Two adults and two children and a driver were on the bus. Two of the adults were taken to a hospital, along with one of the children. The extent of their injuries is unclear.
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A woman driving one of the SUVs involved in the accident had her 3-year-old in the car and said she was very frightened when the accident occurred.
A 16-year-old who was on the bus described the horror of the moment.
"I was having a panic attack, we were freaking out trying to figure out how to get off the bus," he said.
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The windshield of the bus came out as a result of the impact.
The accident disrupted traffic in the area for several hours.