1/7000000000000 or 50/50

[Zersy]

Okay I've been trying to wrap my head around this and cannot make exact logical sense in it. If I were to push a button and the result of doing so shall randomly kill a person in the world what are the chances of it being my best friend ?

My argument is that it would 50/50 of it being my friend since the process is random and no one is favoured in anyway so it is either it is him or it is not him.

2 friends of mine instead say that the chances are 1 to 7 billion (assuming there are still 7 billion people on earth) that someone I know shall get axed from the random process.

I ask you escapist which one is it and why ?

 

[Phas]

If it chooses randomly, it chooses between the 7 billion people on the earth, and he is one person not 4,5 billion people.

Edit: 3,5 not 4,5.

 

[OldKingClancy]

EDITED so people will stop quoting this. I gave my opinion, sorry if anyone disagrees with it.

 

[SaikyoKid]

I would have to say that your friends are right on this one.

Lets compare it to another rather basic example of the marble in the bag. Say you've got a rather large bag that contains 7 billion DIFFERENT marbles. You're allowed to only pick one at random and take it out of the bag. The odds of you picking one specific marble out of that bag is indeed 1 in 7 billion, not 1 in 2.

 

[DEAD34345]

Well, assuming that the chance is completely random, and everyone in the world has an equal chance of being chosen, and you only have 1 friend, then it would be a chance of 1 in 7 billion.

Just because (in your mind) there is 2 possible outcomes does not mean they are equally likely. For example, you either win the lottery, or you don't win the lottery, but chances are far far greater that you won't win.

 

[PhoenixKing]

I can see where you're coming from, but you have to think deeper. So you're saying it's 50/50 because he either will die or won't. However, you need to first think about the chances that he will die, which is 1/7 billion. Because of this, it's not actually a 50/50 chance.

 

[the spud]

1/7000000. Your friend is one person. There are 7 billion people. It kills one of those 7 billion people. Your friend has a 1 in 7 billion chance of the universe picking him. Don't really see where the confusion is coming from.

 

[Deus mortuus est]

To the person who is pushing the button it might seem like a 50/50 chance because when you leave either your friend is dead or he's not, but that's only because you don't see the other 7 billion.
If it's truly random then your friend is one of 7 billion and the chance that s/he dies is 1/7 billion. Not a very big chance, but it's there.

 

[HerbertTheHamster]

2 friends of mine instead say that the chances are 1 to 7 billion (assuming there are still 7 billion people on earth

should be 1 to 6999999999999. None of you are right.

 

[theriddlen]

I think that 1 to 7 billion is right.

If it chooses randomly, it chooses between the 7 billion people on the earth, and he is one person not 4,5 billion people.

Did you just divide 7 by 2 and get 4,5 as a result?

 

[New Frontiersman]

My argument is that it would 50/50 of it being my friend since the process is random and no one is favoured in anyway so it is either it is him or it is not him.

That's not how statistics works... T_T

Under that same logic we could just as easily say it could be me or it could be not me thus it has a 50/50 chance of killing me. We could apply the same argument to anyone, and it would still be just as illogical.
Assuming the button was not rigged specifically to kill your best friend, presumably he would have just as much of a chance as anyone else in the world of being killed, so that would he would have about a 1 to 7 billion chance of being killed, as would everyone else in the world.

 

[WanderingFool]

The way you see it, there is a 50/50 chance, which is right, in a sense.

But the odds of your friend dying are actually the 1 to 7 billion. To you, its a 50/50.

 

[V8 Ninja]

I can kind-of see why you might be confused, but the answer to the question is 1/7,000,000. Now, if the rules of the button stated "either your best friend or any other person in the world will die," then the odds of your friend dying would be 50/50 because the statement is an Either-Or statement.

 

[zehydra]

couldn't say. I've never observed a random system.

the odds are probably 1/7billion-1, but it's pretty much useless trying to predict a perfectly random system.

 

[Phas]

I think that 1 to 7 billion is right.

If it chooses randomly, it chooses between the 7 billion people on the earth, and he is one person not 4,5 billion people.

Did you just divide 7 by 2 and get 4,5 as a result?

Right, sorry, 3,5 not 4,5.

2 friends of mine instead say that the chances are 1 to 7 billion (assuming there are still 7 billion people on earth

should be 1 to 6999999999999. None of you are right.

His friends are obviously super smart sentient hamsters, not people!

 

[Atticus89]

50/50. You either kill him, or you don't.

That's like saying you'll either win the lottery or you won't despite the fact that the chances of you losing is incredibly far more likely.

 

[Caravelle]

The answer is that random events have what's called a "probability distribution". That is, if you have, say, three possible events, they do NOT necessarily have the same probability of happening. When they have the same probability of happening it's called a "uniform distribution", and it's actually rather rare outside of artificial situations like games of chance or math problems.

You can try it yourself if you have two coins. Throw one coin a hundred times : you should get a similar amount of heads and tails if the coin is fair : throwing one fair coin yields a uniform probability distribution.

Now throw both coins a hundred times, and note how many times you get the situations "two heads", "two tails" and "one heads/one tails". You should get about twice as much "heads/tails" as you'll get "heads/heads" or "tails/tails". That's because you DON'T have a uniform distribution of the probabilities over those outcomes. You DO get a uniform distribution if you distinguish the coins from one another and consider "heads/tails" different from "tails/heads", but if you don't distinguish the coins and consolidate those two outcomes into a single outcome, you end up with one outcome having twice the probability of the others.

So here, when you're proposing to kill one random person in all humanity, you do have a uniform distribution... over all humanity. Not over the pair of outcomes "your friend" and "not your friend". The probability of getting the former is 1/7000000000 and the probability of getting the latter is the combination of the probabilities for every other human, i.e. 6999999999/7000000000.

Consider a more day-to-day example : the lottery. If you buy a ticket you can win, or you can lose. So is it 50/50 ? No : there is only one number that can make you win but there are millions of numbers that can make you lose.

In general, remember that "there are two possible outcomes therefore it's 50/50" is simply false. The number of outcomes has nothing to do with the probabilities associated with each - except in the very special case of the uniform distribution.

 

[ChildishLegacy]

The reason you think it's 50/50 is there are two outcomes (for you, looking at it from an outsiders point of view theres 7 billion outcomes). Like a coin flip is around 50/50, as it has two EQUALLY likely outcomes.

But not everything with two outcomes is 50/50, including this one, your friend is one in 7 billion, not one in two, so there's an extremely low chance. In fact, this one isn't two outcomes, it has 7 billion outcomes.

I thought some basic probability and stats was mandatory in maths nowadays anyway?

Edit: Also I'm pretty sure the number they use to count the world population is the 'American Billion', so its 7000000000 (seven thousand million)

 

[Stall]

50/50. You either kill him, or you don't.

That's like saying you have a 50/50 chance of either getting hit by lightening, since you are either struck by a bolt or not. Just because it's a dichotomous set of outcomes does not mean each possible outcome has the same probability of occurring. Those might be the only two possible outcomes, but each outcome has a different chance of occurring. Think of flipping an unfair coin, i.e. one where the probability of getting a head is 0.6 Basically, simple would stipulate that you have a .6 chance to get a heads and a .4 chance to get a tails. But under your logic, you would have a 50/50 chance to get both, despite the coin being unfair.

So yes, it would be one out of every person in the world, since the term "random" implies that each element has an each chance of being selected. So there's effectively a zero percent chance that the button will kill your best friend.

I'm a statistician... you can trust me on this one.