How to calculate “Your odds are 1:xxxx” probability of being involved in a distracted driving crash?

I can't find this statistic online and was wondering if someone can help me figure out how to calculate it from the information I have.

1162 people a day are injured in crashes related to distracted driving. How would use that to find "Your odds of being involved in such a crash are 1: xxxx" informaton? Would I need the total number of cars on the road in a day and divide it by 1162? Or the total number of people on the road? Any suggestions for where to locate such a figure?

Thank you.

EDIT: I've found more data, if that helps. These stats are all for the US in 2012.

The average annual miles driven per vehicle was 12,177. The total miles driven by all vehicles was 2,938,000,000. There were a total of 2,393,561 car accidents and fatalities, of which 424,328 were due to distracted driving.

Seems like I have enough info here, just trying to figure out how to put it together.

If out of $x$ number of people, $1162$ are injured in crashes, then the probability of crashing is $\dfrac{1162}{x}$.
Now the odds of an outcome is just the ratio of the number of successes to the number of failures. Therefore, the odds of an accident are $1162 : x - 1162$ or
$$\Large 1 : \dfrac{x - 1162}{1162}$$