The crash was reported on eastbound lanes just before 11 a.m. near Ramsey Street in Banning, according to the California Highway Patrol.
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The CHP says the Greyhound with 33 people on board was traveling in the second lane about 60 to 65 mph when a left front tire blew out.
The bus lost control, skidded left and hit a Mitsubishi Outlander in the next lane, then struck the center divider.
Authorities say one person on the bus suffered major injuries and another 10 had minor injuries. They were all transported to local hospitals. Two occupants of the Outlander were also brought to local hospitals.
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The remaining passengers were transported to the Morongo Tribal Hall in Cabazon. Nobody was injured in the Mitsubishi.
One lane was blocked on the eastbound 10 as authorities continued to investigate the accident. Traffic is now moving in the area.