Traffic Accidents and Presidents

[Charmed]

Dear Covers:

Good morning. Marc wanted me to provide an exact reference for the automobile accident in Ohio (I think), when there were just two cars in the entire state of Ohio. One day, I remember, reading (I don't know where, now) these two cars came from opposite sides of the same street and crashed into each other. I did go the public library in Troy, and I did find the book where I thought I might have seen this, but I couldn't find the statistic about the historical Ohio two-car crash. But, it was not a wasted trip. I found some other things, I could post here.

The following is from the book The Automobile by Clay McShane (Greenwood Press, Westport, Conn, 1997). McShane gives interesting tidbits chronologically by year. Most are short and highly readable. There a couple here about two U. S. Presidents, Woodrow Wilson and Teddy Roosevelt.

1906: The possession of a motor car is such an ostentatious display of wealth that is stimulate socialism, said Wilson. He was then President of Princeton University.

1912: Teddy Roosevelt injured in an auto accident while campaigning for President.

1913: President Wilson's car hits a messenger boy. Wilson and his chaueffer accompany the boy to the emergency room of a nearby hospital. Wilson promises the boy a new bike.

1916: President Wilson turns down the offer of a free Cadillac, preferring a Pierce-Arrow instead.

There are many more fun facts in McShane's book. I will keep looking for the Ohio two-car crash story.

Anyways, what is the probability that if there are two and only two cars on the road, that the two cars would be in a head-on collision? Anyone ready to a take a guess on that probability question instead?

Charmed

[D.Scott]

Assuming the two cars were on the same road and headed in opposite directions, the probability they would be in a head-on collision would be 50/50. They would either hit or miss each other. No other possibilities exist.

Am I missing something?

Dave

[Tim Folkerts]

Dave,

I'd never drive a car if the odds were 50/50! That would mean that half of the time I would hit any car I met head on. You couldn't expect to go more than a mile or two without a collision.

I have been driving for over 20 years, at about 20,000 miles per year, which is 400,000 miles. Suppose 1/2 of that is on two lane streets, and I meet 5 cars per mile. The makes 1,000,000 miles. Supposing I might expect 1 collision in that time, then the odds are about 1 PPM = 1/1,000,000. One out of a million times I meet a lone car on a two lane road I might expect a collision (give or take a factor of 10).

Tim F

[D.Scott]

Tim, What would you say are the possible events of two cars heading toward each other on the same road? Forget all the interveining actions like driver awareness, corrections, automatic reactions etc. Just 2 cars headed toward each other. What are the possibilities? They will hit - they will not hit. Any others? If not, the chances of any 2 cars headed toward each other with no outside influence hitting each other has to be one out of two possibilities or 50/50. The number of times you have passed a car successfully has nothing to do with the basic probability. They will either hit or not hit. Each occasion is the same. The probability is always 50/50.

Now, you want to talk real life with all the events that can change the probabilities, I will agree with you but take everything else away except two cars headed toward each other on the same road and they are either going to hit or they are not going to hit.

I don't want to scare you but taking your example, you had better expect that any one of those 1,000,000 approaching cars could hit you and be prepared to take some action. If cars didn't have all the nice "avoidance devices" like lights, steering, brakes and accelerator, let alone all the driver actions, we might be looking at a lot more chance encounters on the road.

Dave

[Wes Bucey]

In Reply to Parent Post by D.Scott

Tim, What would you say are the possible events of two cars heading toward each other on the same road? Forget all the interveining actions like driver awareness, corrections, automatic reactions etc. Just 2 cars headed toward each other. What are the possibilities? They will hit - they will not hit. Any others? If not, the chances of any 2 cars headed toward each other with no outside influence hitting each other has to be one out of two possibilities or 50/50. The number of times you have passed a car successfully has nothing to do with the basic probability. They will either hit or not hit. Each occasion is the same. The probability is always 50/50.

Now, you want to talk real life with all the events that can change the probabilities, I will agree with you but take everything else away except two cars headed toward each other on the same road and they are either going to hit or they are not going to hit.

I don't want to scare you but taking your example, you had better expect that any one of those 1,000,000 approaching cars could hit you and be prepared to take some action. If cars didn't have all the nice "avoidance devices" like lights, steering, brakes and accelerator, let alone all the driver actions, we might be looking at a lot more chance encounters on the road.

Dave

I don't normally enter into these debates about statistics, but it occurs to me to make a differentiation between "probability" and "possibility" - Certainly, the possibility is narrowed to two outcomes - the vehicles will collide or not collide, regardless of the direction of travel. Factors for probability include direction of travel, speed, driver ability, weather and visibility conditions, vehicle condition, etc. ad nauseum.

[D.Scott]

Wes - I agree there are all sorts of factors that could influence the outcome but the original question was simply stated as 2 cars coming toward each other - what is the probability they will hit head on?

For this question I submit that adding nauseum or anything else would assume extra conditions and therefore spoil the batter. In the quality industry we all know if we assume we make an *** of u and me.

Dave

[Wes Bucey]

In Reply to Parent Post by D.Scott

Wes - I agree there are all sorts of factors that could influence the outcome but the original question was simply stated as 2 cars coming toward each other - what is the probability they will hit head on?

For this question I submit that adding nauseum or anything else would assume extra conditions and therefore spoil the batter. In the quality industry we all know if we assume we make an *** of u and me.

Dave

Yeah, but why not work with a real world example?

This seems to me similar to physics problems from high school which ignored "friction."

In theory, all my computer-controlled machining centers would turn out perfect material every time. They came close, but not 100%. What about root cause, common cause, and any anomolies?

[Tim Folkerts]

Dave,

As Wes said, there is a big difference between "possibility" and "probability".

Saying the odds are 50/50 implies that a) there are two possibly outcomes and b) the two outcomes are equally likely. Just because a) is true doesn't mean b) is true. To find the probabilty, you need to determine the likelyhood of the outcomes. Probabilty always deals with circumstances - either repeating an action like flipping a coin, or making estimates based on reasonable assumption. I suppose if you knew nothing about the actual situation, then 50/50 is the best guess - you can't be more than 50% off from the correct answer.

For example, suppose there are 2 seconds left and your basketball team is down by 1, and you are shooting two free throws. Would you say "it doesn't matter who shoots, because it either goes in or it doesn't, so the odds are always 50/50." Or would you say "Put the best shooter on the line because he has a much better than 50/50 chance of hitting the shots."

Or a second example. A part comes off the assembly line and is tested with a go/no-go gage. Are half of all parts automatically bad just because there are two options?


Tim F