The projectile does not hit 2 times in one place - but what about from the point of view of probability theory?

Question

Mathematics

There is such a soldier's belief that a shell does not hit the same place 2 times, so a fresh funnel was considered the safest place under shelling.

It seems to me that it all depends on the density of shelling ... How is this explained from the point of view of probability theory?

Have you seen this example in the literature? What to read on Terver in such an applied form?

Answer 1

You can also hide in a funnel because fragments are the main damaging factor.

Answer 2

Look at the whole theory according to the words "scattering ellipse", but in a nutshell here .

Answer 3

Probability theory studies probabilistic models, so in your case everything depends on the chosen model. If the enemy shoots methodically at the same point, then the statement is obviously false. If there are several points with a non-zero probability of hitting them, then it is obvious that if we take p as the probability of hitting some chosen point, then the probability of hitting it twice in a row will be p² < p .
However, these are "a priori" probabilities. Those. it is assumed that the event we expected (two hits in a row) has not yet happened. If we already know that the projectile hit a certain point, then this has nothing to do with the place where the next projectile hit. Another important feature of the model is the independence of events. Again, if the shelling is carried out in such a way that not a single point is covered twice, then indeed, you can hide in a funnel :-)

Answer 4

I think it’s not worth excluding a hit, but the probability is definitely reduced due to various factors

Answer 5

Here the random number generator is the atmosphere (the shape and weight of the projectile can significantly reduce the influence of the atmosphere), the temperature of the barrel, the amount of explosives, the quality of the explosives, I don’t know how the reaction of the explosion develops, but I assume that this can also affect accuracy, the ideal aerodynamics of the projectile is not perfect (there may be an influence, but the influence is extremely small due to the large weight and specially designed shape), barrel wear (well, it wears out).
The probability of hitting 1 gun in the same place is about the same as rolling a die and rolling the same number as before. Only the faces of the cube should be correspondingly larger. And the hit sectors should not be uniform (less in the center at the edges more).
The question looks like this: If you roll a die and you roll a 6, what is the probability that the next roll is a 6?
The answer is exactly the same as last time. BUT something depends on the temperature of the barrel.
As for the art upstrel, with dense fire, mostly shells fly into small

Answer 6

Wikipedia about the Battle of Jutland:

The British adopted a volley-hunting tactic, directing the cruisers directly to where the enemy salvo had landed. The saying that a shell does not hit the same funnel twice turned out to be true, and the cruisers did not receive serious damage, although they were forced to zigzag.

Answer 7

It has already been mentioned above, but I would like to highlight it separately: the belief about funnels, as well as about lightning that does not strike twice in one place, are special cases of " Player's mistake " (you can google by name for a more complete description). Naturally, this is “in a spherical case in a vacuum”, in practice hundreds of additional factors influence each individual case.

Answer 8

From the point of view of probability theory, this cannot be explained in any way, since it is not a random number generator that comes out of the cannon.

Answer 9

it's 50/50 - either it hits or it doesn't. so it doesn't matter where you hide.

Answer 10

Strictly speaking, this is not fair for mortar shelling. The probability of a repeated hit of a mine in a circle of small radius in the absence of guidance adjustments is more than 70%.