EASY statistical problem that seem very HARD at first glance

[no gnu taxes]

Imagine a number of baseball pitchers standing randomly in a baseball field. For ease of argument, imagine both the number of pitchers and the size of the size of the field are infinite.

Okay, at a given signal, each throws a fastball at the head of the nearest pitcher and kills him. The question: After the throws, what portion of the pitchers will still be alive?

While this is not a hard problem, it will require a basic knowledge of calculus priniciples or at least pre-calculus elementary functions knowledge to solve it independently.

[str]

Imagine a number of baseball pitchers standing randomly in a baseball field. For ease of argument, imagine both the number of pitchers and the size of the size of the field are infinite.

Okay, at a given signal, each throws a fastball at the head of the nearest pitcher and kills him. The question: After the throws, what portion of the pitchers will still be alive?

While this is not a hard problem, it will require a basic knowledge of calculus priniciples or at least pre-calculus elementary functions knowledge to solve it independently.

Guess they should have worn a helmet.

[stuntin909]

none?

[dodger33]

10%

[TankHankerous]

I like turtles.

[slambam]

I don't know shit about calculus, but "logic" would say 0, since most would be throwing at each other (player A hits player B and player B hits player A). But there are circumstances where one player would throw at somebody, but nobody would throw at him. I'm sure these answer is 0, since there is an infinite number or players, but either way, calculus or no, it would be impossible to know.

[Boner_18]

whatever the asymptote of that curve is.

[wantitall4moi]

if they arent standing in a circle one pitcher will be left alive....the one furthest to the right.

I imagine the 'correct' answer is supposed to be zero however.

[no gnu taxes]

Say the number of pitchers is "x."

Lets look at any one particular pitcher, which could be any pitcher, and if he gets hit by one OR more of other pitchers, then he is dead.

The number of pitchers other than this one is x-1.

Follow me so far?

So let's find the likelihood a pitcher will hit another pitcher other than the one in question.

Pick any one of the x-1 pitchers other than the one in question.

What is the likelihood that this pitcher will be hit the one in question?

Well, since the number of total other pitchers than the 2 listed (the one in question plus any given pitcher who might hit him) is x-2, then the chance of any other pitcher hitting some pitcher other the one in question is (x-2)/(x-1).

Ok, since there are x-1 other pitchers, the chance that no other other pitcher will hit the one in question ((x-2)/(x-1))^(x-1)

There are an infinite number of pitchers.

So the only thing left to do is solve the problem as x goes to infifnity which is where the calculus principles come into effect (actually it's pre-calculus -- the idea of limits)

[frizzelli]

Think tank this bullshit thread.

[mathdotcom]

Statistical 'puzzles' involving infinity are rarely interesting

They usually just make use of the property that for any continuous x the probability of x = x-hat is 0

If you said the number of pitchers is very large but finite then there's nothing interesting going on

[JohnGalt2341]

I can't decide if I'm over thinking this or under thinking this. So... no 2 players would be throwing at the same player? If that's the case I don't see how the answer wouldn't be zero. If it isn't the case then I don't see how you could possibly come up with an answer.

[mathdotcom]

I think the original post is wrong

Any pitcher can kill any other pitcher, not just the nearest one

[trytrytry]

easy 3

[Chi_archie]

this is the kinda thread PavyRacer was born to post in

[RudyRuetigger]

0, the balls never get to the other person

[FindTheLock]

all of them = ∞

[mathdotcom]

0, the balls never get to the other person

A continuum of pitchers with zero mass can't throw the ball very hard

[FindTheLock]

If you are aiming at someones head while they are standing still, you will not hit their head after they have gone through the throwing motion.

[SteelRain]

my guess is 0

limit of 1/x = 0
as x approaches infinity

[face]

not enough information. the key piece of information is the word "nearest". since i have no way of knowing this, i have no way of knowing how many pitchers will double up on other pitchers and leave certain pitchers alive.

[DoctorPhil]

DOCTOR Ph1LZ SAYS THIS QUESTION IS FAIL.

TAKE 4 PEOPLE in a LINE EQUALLY SPACED APART.

1 2 3 4

1 throws at 2
4 throws at 3
2 can throw at 1 or 3
3 can throw at 2 or 4

IN ANY EVENT, in this example there can be 0,1, or 2 LEFT

FKKKKKKKKK FAIL

[PharaohUB]

If it's an infinite amount of pitchers then they have an infinite number of people tied for how close to any particular pitcher. Because it's infinite then your dead someones going to shoot you. Everyones dead. Answer is zero as you approach infinity. No gnu's formula goes to zero as you approach infinite, so i guess i'm right.

[no gnu taxes]

The limit of ((n-1)/n))^n as n goes to infinity is 1/e.

[Hawkeye2011]

this thread is gay

[Ghenghis Kahn]

math is idiotic. the answer is 0.

/thread

[RudyRuetigger]

infinite pitchers inside the infinite field means infinite space inside the field and the pitchers arent throwing infinite distances

[riffraff24]

Is this real life?