A train will pass the same point every 7.5 minutes everyday of the week from 4am to 8am. There are 3380 vehicles traveling west bound on a road that is adjacent and parallel to the train tracks every day. What is the probability that one of those vehicles will leave the road and land on the train tracks where the train will collide with the vehicle? ]]>

where , and are (doubly truncated) Gaussians with the same mean and different variance, and are the truncation points.

To start off, I wrote:

where

At this point I'm absolutely stuck. Is what I wrote correct? Is there any other way to derive the result more directly?

I've attached a Pdf as well for you to see the formulas more clearly, if needed.

Any help and advice would be GREATLY appreciated.

Sorry for my poor english, I´m from Argentina.

And sorry too if I´m in the wrong place.

I need some knowledged about stats and this forum is what seems the best I could found for my needs, but not sure.

To the point:

I have an experiment with two possible results: A and B

I did the experiment 100 times and gives me results A 52 times and B 48 times.

In the other hand, I have another experiment with results C and D.

I did this experiment 100,000 times and gives me 51,000 times C and 49,000 times D.

Now I need two options for a one chance bet: A vs B is one option and C vs D is the other option.

Of course in case of the first option I must bet for A and in the second option I must bet for C.... but my question is... wich option I must choice:

A vs B or C vs D?

I´m prety sure I must choice C vs D no matter here the probabilities are 51% vs 49% instead of 52% vs 48% as it is in option A vs B cause I think the previous results had less possibilities to be just cause luck in second experiment than in first experiment. .... but I´m not able to cuantificate why that choice.

Thanks for any help and for your time! :) ]]>