SharpsDressedMan
Anyone care to calculate the odds of a random shot hitting a slow moving target, sight unseen, from a mile and half away, in the dark, where very few people might be at the time (a back country road at 10:00 at night)? My guess is that God could have easily intervened, as could fate, and that that young girl is with God now. Had that horse been one step ahead, or behind, the bullet would have missed. '
Yeah, I tried to make a start on that and discovered there were too many assumptions that had to be made.
I started out on a linear basis,where the circumference of a one mile circle was divided by the
length of the human head from nose to back of the head, which gave me odds of about 44,000 to one for the one mile circle and about 66,000 to one for a 1-1/2 mile circle.
Sample calculation on that aspect of it that I did last night:
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Figuring the head is about 0.75 feet in length, nose-to-occipital bone, and the circumference of a one mile radius circle is 33,175 feet, that makes the odds of hitting someone's head anywhere on that circle by a random shot are 44,234 to one, if it is known that the bullet will impact the ground at that range with some given elevation.
33,175 / 0.75 = 44,234 ( P = 2.3e-5)
For a 1-1/2 mile circle, it's 66,350 to one. ( P = 1.5e-5)
(Note that I did not actually post that.)
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The assumption there was that the gun was fired at an
known elevation to have the bullet come down exactly one mile from the firing point and exactly 1-1/2 miles from the firing point respectively, but fired in a random
direction.
The next step would have been to figure the odds of the gun being fired at a
random elevation to have the bullet land in the
vertical dimensions of the human head at those distances and then multiply the two probabilities, that is:
The odds (1 / Probability 1) of firing in the exact
direction required.
multiplied by
The odds (1 / Probability 2) of firing at exactly the right
elevation required.
With both random elevations and directions, this would have given the probability of hitting the
area of the human head at those respective distances.
I think.
We can ignore the movement of the "target," since this all occurs in one instant of time and it was not an aimed shot for which "target" movement during the bullet flight would have been relevant.
I think.
However, this ignores the fact that the "random elevation" can't be truly random, since it is known that a bullet fired either straight up or absolutely horizontally would not reach those ranges. Thus, this "random elevation" must actually be restricted to elevations which
might give ranges like that, say between 25 and 35 degrees-ish.
I think.
Note the "ish."
I gave up and went to bed at that point and decided to leave it to the actuaries among us.
Terry, 230RN