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Tire Blowouts are unfortunately one of the top causes of auto accidents.  The number of incidents has decreased in recent years because of improving tire technology.  One of the main reasons why tire blowouts cause accidents are because most drivers will not react properly when it happens and tend to panic, losing control of the vehicle.
Race car drivers and police officer are trained for tire blowouts and know the best way to control the vehicle when it happens.  In the split second that a tire blows out, an average driver may slam on the brakes which can actually cause the vehicle to lose control because of the sudden imbalance.  The best way to control it is to actually maintain the same speed or even accelerate slightly, stay straight, and then slow down and pull off the right side of the road.
Having properly inflated tires can drastically decrease your chances of getting a blowout.  Check them monthly and don't drive with old worn down tires.
Keep a tire air compressor handy to help you get into the habit.
Of course, some things may be out of your control such as potholes and sharp objects that can puncture your tires.  However, preparing ahead of time, keeping a safe distance from cars ahead of you, , not panicking, can help you avoid accidents from a blowout.  
This video shows the practical steps to take should a blowout occur: