1/7000000000000 or 50/50
- Thread starter Zersy
- Start date
I think we can safely assume that this is an estimation and you are not properally taking significant figures into account, since I am quite sure that even if it was 1 short of a full 1 to 7 billion, by the time you finished writing your response, that 1 more person was born.HerbertTheHamster said:
It's not that it's either him or not him, it's that it's either him, or that guy, or that guy, or that guy, or that guy, etc. If you're rolling a 6-sided die, the odds of any one side is 1/6. Six sides, one side can come up. The odds of rolling a 4 aren't 50/50, because there are five other ways it could end up. Now picture that every person on the planet was assigned a number, and a die with that number of sides was rolled, selecting one person at random. The odds of it being any single person are 1/X, where X is the population of the world.
Statistically you'd have a one in seven billion chance at killing your friend. Karmically, you'd have a one in two chance of killing your friend and a one in two chance of killing a family member.
That's not how it works.OldKingClancy said:
Say there are 7 billion people on the planet exactly, and the button will kill one person completely at random, the friend's chance of dying is 1 in 7 billion; the same as everyone else's chance. If it was between his friend and one other person, then it would be 50/50.
Maybe you and the OP are confusing an equal chance with 50/50. Its still equal if everyone on the planet has a 1 in 7 billion chance of dying.
Kudos on the Kate Upton pic though.
You seem to be doing the same; it has to be the same number of people on either side for it to be 50/50.Vhite said:
The 50/50 refers to the actual numbers, not the "he's dead or he's not" aspect. Its not "him or not", its "him or one of the other 6,999,999,999 other people".
1 for every single person you care about to the total world population, reduce as possible.
For the sake of the argument, let's say the people you really, really don't want to die total, and I'm just picking an easy number here, 50. Let's guesstimate about 7 billion people besides you with beating hearts on this planet. 50/7,000,000,000. Reduce, we get 1/140,000,000.
Those are the odds that pressing the button will kill a loved one. However, if we word it just a little bit differently, things get confusing. Instead of "what are the odds the random person will be a loved one?" we say "this button will either kill a loved one, or it won't." The difference is the complete disregard for probability.
Personally, I like them odds.
For the sake of the argument, let's say the people you really, really don't want to die total, and I'm just picking an easy number here, 50. Let's guesstimate about 7 billion people besides you with beating hearts on this planet. 50/7,000,000,000. Reduce, we get 1/140,000,000.
Those are the odds that pressing the button will kill a loved one. However, if we word it just a little bit differently, things get confusing. Instead of "what are the odds the random person will be a loved one?" we say "this button will either kill a loved one, or it won't." The difference is the complete disregard for probability.
Personally, I like them odds.
Imagine you had a bag with a red ball, a yellow ball, a green ball, and a blue ball. You get to pull one ball out at random.
Do you really think the odds that it will be a red ball are 50/50, because it is either a red ball or not? Of course not, your choosing one of 4 options, not one of 2. So the odds are 1/4.
Similar picking a random person in the world would be 1/population of the world. Of course, the guy who gave you the switch could be giving you loaded dice, in which case its surely gonna be your friend.
Do you really think the odds that it will be a red ball are 50/50, because it is either a red ball or not? Of course not, your choosing one of 4 options, not one of 2. So the odds are 1/4.
Similar picking a random person in the world would be 1/population of the world. Of course, the guy who gave you the switch could be giving you loaded dice, in which case its surely gonna be your friend.
The chance is number of people you know / number of people on earth. Unless you know half of the world's population the 50/50 thing makes no mathematical sense whatsoever.
EDIT: Oh, I misread you post. Assuming you have one best friend, the chance is 1 / number of people on earth.
EDIT: Oh, I misread you post. Assuming you have one best friend, the chance is 1 / number of people on earth.
Here's how you solve this problem.UNKNOWNINCOGNITO said:
Enumerate the state space.
Count the number of states in which the outcome you're querying happens, versus the total number of states.
Take the ratio of the success to total state counts.
The result is the probability.
The natural reading of the problem you've phrased suggests a state space that assigns one state to each person dying.
So the chance of it being your best friend is exactly 1/(|world population|).
However! There is also the possibility that you might want more dense state space. In this version, potentially more than one person can die. If you assign equal probability values to the cases where, for example, "Person A dies alone", "Person A and Person B are the only ones to die", "Person A and Person C are the only ones to die", "Person A, B and C are the only ones to die" and so on, and do not distinguish between the states where "Person A and Person B are the only ones to die" and "Person B and Person A are the only ones to die", then you will find that the probability of any given person dying is independent of the probability of anyone else dying, and your intuition would be correct.
In conclusion, it all depends on your enumeration of the state space in interpreting a "random distribution".
Sorry to quote again, but here's an easy test of whether your intuition works in this case.UNKNOWNINCOGNITO said:
Does the problem accept that there is a very small chance that everyone on the planet might die as a result of the one button press?