Maths nerds

[Brett_J]

Ok read an article recently about shooting/snipers.

Anyway, the journalists claims over the distance with the gun and conditions, that the shooter has 5% chance of hitting the target, so they used 2 shooters, which gave them a 10% chance.
It's been a very long time since i was in school - nearly 20 years, lol. But from what I remember probability isn't cumulative in this case.

I seem to remember it being multiplied by the chance of target ebeing hit and the chance it isn't and the shots fored, in this case 2, as each shooter fired once and one shot killed the target.

So
2 shooters
2 Shots
5% chance each of hitting target
1 Shot hit target.

Whats the probability of the target being hit.

I don't know if I explained it right, because Tradie :P

[duste]

Been a while since I've done probability...but pretty sure 0.05+0.05=0.10=10% is correct, given they're talking about the chance/probability of Shooter A or Shooter B hitting the target.

If they were talking about the chance/probability of Shooter A and Shooter B hitting the target, then 0.05*0.05=0.025=2.5% would be the correct answer.

[Bomber]

Both shooters have the same probability of hitting the target given all the same conditions = 5%

[Brett_J]

Been a while since I've done probability...but pretty sure 0.05+0.05=0.10=10% is correct, given they're talking about the chance/probability of Shooter A or Shooter B hitting the target.

If they were talking about the chance/probability of Shooter A and Shooter B hitting the target, then 0.05*0.05=0.025=2.5% would be the correct answer.

I'm going off the second, if the forst was the case then if they had 20 shooters with 5% chance of hitting the target, then it would be 100%
I didn't think probability was cumulative?
But I'm far from any sort of maths guru, I'm more asking than guessing.

[volt_bite]

The probability of hitting it with 2 shooters is still the same as Bomber mentioned. But the chance of hitting increases.

Its just like if you have x100 50% bets to win. Each bet has a 50% probability of occurring or winning. But the more you bet the more chance you have to win.

The probability of the 100 bets all winning on a 50% chance probability, thats when you multiple the probability together as Duste mentioned.

Statistically speaking you have a better chance of hitting the target with more shooters than you do with just one.

[duste]

I'm going off the second, if the forst was the case then if they had 20 shooters with 5% chance of hitting the target, then it would be 100%

Meaning it is highly likely the target would get hit at least once after all the shooters have had their go.

Practical example: You and your partner are trying to have kids. Assuming your last name isn't Fairchild, it's not going to be a 100% success rate, but it's going to be a hell of a lot more likely the more times you shoot your bullets.

EDIT: I think we're getting confused; the individual probability of a shooter hitting the target does not change, but the combined probability of the target getting hit by a shooter does.

[Brett_J]

Meaning it is highly likely the target would get hit at least once after all the shooters have had their go.

Practical example: You and your partner are trying to have kids. Assuming your last name isn't Fairchild, it's not going to be a 100% success rate, but it's going to be a hell of a lot more likely the more times you shoot your bullets.

EDIT: I think we're getting confused.

The individual probability of a shooter hitting the target does not change, but the combined probability of the target getting hit by a shooter does.

Bad analogy to use on me :P

Yeah I get ya.

[Brockas]

Easiest way to explain:

5% = 5 out of 100 shots will hit the target.

Shooting twice doesn't change that percentage.


Taking two shots doesn't meant there's a 10% change of the target being hit, it just means that if both miss probability tells us that 5 out of the next 98 will probably hit.

[volt_bite]

Here is another example:

If shooter one takes 100 shots and he hits 5 targets, that's a 5% probability
Now shooter two takes 100 shots and he hits 0 targets, that's a 0% probability
Overall shots taken = 200 shots, 5 targets hit = 2.5% (5/200) overall probability.

If both shoots have 100 shots and both hit 5 targets (ie equal probability).
Overall shots taken = 200 shots, 10 targets hit = 5% (10/200) overall probability

However 10 targets are hit as opposed to only 5 targets (ie as if only one shooter). Overall you hit more targets.

[R3N]

5% is 5 out of 100, but is also 10 out of 200, so if each sniper shoots 100 times each, they have the same 5% probability.

The more you shoot, the more chances of it hitting, but it doesn't increase the probability.

[schnoods]

If you have twice as many bullets flying at a target, you will double your chances of hitting the target, it still might be 5% accuracy but it will double the chance.

Mathematically its still 5%, but in a real world situation where you are covering more ground, different angles etc, i dont know how a nimrod journalists comes with those facts and figures.

[DBLDOSE]

Possible outcomes:
Shooter 1 & 2 both hit - 0.05 * 0.05 = 0.0025, 0.25%
Only 1 shooter hits - (0.05 * 0.95) + (0.05 * 0.95) = 0.0475 + 0.0475 = 0.095, 9.5%
Both shooters miss - 0.95 * 0.95 = 0.9025, 90.25%

Therefore, if both shooters fire once, the chance for the target to take a hit is 9.75%.

Edit: Should learn to read OP...

16 possible outcomes from 2 shooter firing 2 shots each, taking each shot as in individual event:
All 4 shots hitting is 1 outcome
All 4 shots missing is 1 outcome
Combinations of 3 shots hitting and 1 missing is a total of 4 outcomes
Combinations of 3 shots missing and 1 hitting is a total of 4 outcomes
Combinations of 2 shots hitting and 2 missing is a total of 6 outcomes

4 shots hitting = 0.05^4 = 0.00000625, 0.000625%
4 shots missing = 0.95^4 = 0.81450325, 81.450625%
3 shots hitting = 0.05^3 * 0.95 * 4 = 0.000475, 0.0475%
3 shots missing = 0.95^3 * 0.05 * 4 = 0.171475, 17.1475%
2 shots hitting = 0.95^2 * 0.05^2 * 6 = 0.0135375, 1.35375%

Therefore, chance the target will take a hit is 100 - 81.450625 = 18.549375%

[JBAE]

If the player enters the correct password in the console then hit probability is 100% and all headshots.

Simple.

[Brett_J]

Possible outcomes:
Shooter 1 & 2 both hit - 0.05 * 0.05 = 0.0025, 0.25%
Only 1 shooter hits - (0.05 * 0.95) + (0.05 * 0.95) = 0.0475 + 0.0475 = 0.095, 9.5%
Both shooters miss - 0.95 * 0.95 = 0.9025, 90.25%

Therefore, if both shooters fire once, the chance for the target to take a hit is 9.75%.

Edit: Should learn to read OP...

16 possible outcomes from 2 shooter firing 2 shots each, taking each shot as in individual event:
All 4 shots hitting is 1 outcome
All 4 shots missing is 1 outcome
Combinations of 3 shots hitting and 1 missing is a total of 4 outcomes
Combinations of 3 shots missing and 1 hitting is a total of 4 outcomes
Combinations of 2 shots hitting and 2 missing is a total of 6 outcomes

4 shots hitting = 0.05^4 = 0.00000625, 0.000625%
4 shots missing = 0.95^4 = 0.81450325, 81.450625%
3 shots hitting = 0.05^3 * 0.95 * 4 = 0.000475, 0.0475%
3 shots missing = 0.95^3 * 0.05 * 4 = 0.171475, 17.1475%
2 shots hitting = 0.95^2 * 0.05^2 * 6 = 0.0135375, 1.35375%

Therefore, chance the target will take a hit is 100 - 81.450625 = 18.549375%

No you were right initially, just a total of 2 shots were fired, which brings it back to the 9.75%

Which is what I go from doing it my weirdly explained way originally.

If each has a 5% chance, then the chance that exactly one sniper hits and one misses = 0.05 x 0.95 x 2 = .095, or 9.5% . The probability that both hit is .05 x .05 = .0025, or .25%. These add up to .0975, or 9.75%,

I work out shit weird in my head, so I could way off, but I am a dumb ass mechanic, I can plead ignorance :P

[Fukushima]

http://graphics8.nytimes.com/images/2013/02/03/us/politics/03skeet_image2/03skeet_image2-articleLarge.jpg


Obama does not miss

[404]

And here I was thinking that it was a standard tactic on a high value target to send 2 snipers loose at the same time that way neither of them would know who's actual shot hit... but clearly it was a maths equation.

[beatle]

Is there a grassy knoll coefficient?

[AdN]

They should just employ 20 shooters