[YeGoblynQueenne]

>> Similar if you drive 1 million km and kill 1 person, if I drive 10 km and kill 1 person is still 1 data point and I can make no conclusion?

Yep. Because I still have another 9 m km to go before I've driven as long as you have and there is no way to know whether I'm going to kill another 9 people, or 0 more, until I've actually driven them all.

[simion314]

You are wrong, there is a conclusion we can make, the conclusion is not absolute but fuzzy so maybe fuzzy logic is not your thing.

Also you have a mistake in your comment, I would still have to do 999990 km of driving. If I killed a person in my first 10 km what is the probability that I won't kill anyone in my next 999990?

Your point is that I can't be 100% sure and that is true but we can compute the probability, so the probability that I had bad luck is very small, if the probability of killing 1 person in 1 mil km is 1 or 100% what is the probability of killing this person in my first 10km? ( you are correct is not 0 )

[YeGoblynQueenne]

I misread the numbers in the original post. But what you say in your comment- well, that's not how it works.

To assess the risk posed by a driver, you wouldn't follow them around, constantly logging the miles they drive, counting the deaths they cause and continuously updating the probability they will kill someone, at least not in the real world (in a simulation, maybe). Instead, what you'd do is wait for enough people to have driven some reasonably significant (and completely arbitrarily chosen) distance, then count the fatal accidents per person per that distance and thereby calculate the probability of causing an accident per person per that distance. That's a far more convenient way to gather statistics, not least because if you take 1000 people who have causd an accident while driving, they'll each have driven a different distance before the accident.

So you might come up with a figure that says "Americans kill 1.18 people every million miles driven" (it's something like that, actually, if memory serves).

Given that sort of metric, you can't then use it for comparison with the performance of someone who has only driven, say, 1000 miles. Because if you did, you would be comparing apples and oranges: 1 accident per 1000 miles is not on the same scale as ~1 accident per million miles. There's still another 999k miles to go before you're in the same ballpark.

And on that scale, no, you can't know whether an accident in the first 1000 miles will be followed by another in the next 1000 miles. Your expectation is set for 1 million miles.

It's a question of granularity of the metric.

[simion314]

Do you have any math do back up that what I said is wrong? I can try to explain my point better but I see you are ignoring the math so maybe I should not waste my time.(we can reduce the problem to balls in a jar and make things easy)

But think about this, if I killed a person in my first 10 km of driving, what is the chance that will kill 0 after the next 999990, would you bet that I will kill 0 or 1 , more then 10?

[YeGoblynQueenne]

I think what you mean by "maths" is "formulae" or "equations". Before you get to the formulae, you have to figure out what you're trying to do. If the formulae are irrelevant to the problem at hand you will not find a solution.

As to your question- I wouldn't bet at all. There is no way to know.

Here's a problem from me: I give you the number 345.

What are the chances that the next number I give you is going to be within 1000 numbers of 345?

[simion314]

Your problem is not equivalent with what we were discussing about, you need to change it a bit like

I draw random numbers from 0 to Max and I get 345, what is P that next number N is in 100 range near 345?

P = 200/Max; in the assumption that Max >445;

For self driving cars, the probability that a car kills a person for 1 km or road driven is unknown, so you can call it X

Then my self driving car killed a person in first 10 km, What is the probability that a random event will happen in the first 10km from 10^9 km, is 10^(-8)

Say the self driving car would have the probability of killing N people for 10^9 km, this are random,independent events So the probability that a kill will happen in first 10km is N*10^-8,

I hope you notice my point that we can measure something, we do not need to wait for 10 or 100 people to be killed

We are not sure but we can say that is is a very small chance that I will not kill other person in my next 999 990km.

let me know if my logic is not correct, in statistics is easy to do mistakes.