Hypotheticals

1. 

The world's best neurological researchers have developed a microscopic device that, if implanted in your brain, will bestow you with superhuman cognition. (Think: the effects of the pill in "Limitless," only without the downside). The catch is that, every day for the rest of your life, the device has a .0001% (1/10000) chance of malfunctioning. If it malfunctions, it will poison and kill a large portion of your brain, rendering you functionally and irreversibly retarded.

Would you volunteer to receive the device, assuming you will receive the only one in existence, and assuming that it cannot be removed once implanted? Why, or why not?

2.

A genie offers you a bargain. For five years of your life, you will become the richest and most famous rockstar on the planet. Your life will be epic beyond your wildest imagination. Immediately upon the conclusion of that five-year period, you will suffer a humiliating public disgrace, lose your fame and fortune, and forever be a cautionary tale, and your name a household curse word. Do you accept the deal?

3.

You meet the girl of your dreams. She is ridiculously beautiful, brilliant, successful, witty, charming, sexy, and so forth. You will never meet another woman who comes remotely close to matching her in any of these qualities and more. Unfortunately, she has a sexual predilection for her own feces. She insists that the only way she can have sex is if she craps in the bed and lets it sit there while you fuck. You can clean it (and each other) up before or after the sex, but she shits the bed every time before the sex begins. Is this a dealbreaker?

Quote:

Originally Posted by MrG 


I'm not saying there's not a good reason out there for making this decision, but you're not choosing based on sound math. You're not being given 27 years; you're being given an opportunity that carries with it a 1/10,000 risk of catastrophic failure. The likelihood of the device failing is no different in 27, or 50, or 500 years than it is in the moment after it's implanted.

The first part of your statement is accurate, but the second part isn't. Probability is distributed over n days, such that the probability of no failure within n days is given by the equation P = (1 - .0001)^n, or .9999^n.

Over a 100 day period, P of no-failure = (.9999)^100 = .990049339.

Over a 5,000 day period, P = .606515496.

Over a 10,000 day period, P = .36786, meaning that the odds the device will not have failed within 10,000 days are roughly 37%, so the odds of at least one failure in 10,000 days are 1-.37, or 63%. It's more likely than not that the device will have failed within that period.

While it's technically incorrect to say that there will be a failure within 10,000 days (a little over 27 years), it's 63% likely that a failure will occur within such a timeframe. The longer the period of time, the more probable that a failure will occur within that period. (The odds of at least one failure hit 86% within 20,000 days, and so on).

Quote:

Originally Posted by MrG 


Yes, the likelihood of it occuring once increases, but the probability of it happening on any given day never changes. That is, over time the probability that the event will happen once approaches 1, but the probability of it happening on day X remains constant (i.e. the device never becomes "due" for failure).
No, my statement is correct in its entirety, but that's because I was talking about the probability of it happening on a given day, not the probability of it ever happening. See my response to munchausen for clarification.
The point I was trying to make is the statement that you're "being given roughly 27 years" is incorrect, because there's nothing that makes it more likely you'll get 27 years than it is that you'll get 30 seconds.

I don't think anyone was ever making the claim that the specific probability changes on Day 10,000. If you got that impression, than I'll accept that I worded my original post clumsily. But that wasn't the intent of my original statement, and I don't believe (?) it was Munchausen's.

The "you have 27 years" is technically incorrect, and I'll concede that much. When I saw the post earlier this morning, I was pretty tired and not-yet-caffeinated, and I sort of went with it without crunching the numbers.

EDIT: I also noticed I made a typo in the OP on this thread, when I said ".0001% (1/10000)." That's a fuckup on my part. I didn't mean to say .0001%, but actually, .0001, which is .01%. It seems nobody (myself included) noticed the typo, and thus, it didn't really change the nature of the discussion.

All of the stats debate aside, what are your answers to the quandaries? ^_^

Moar:

4.

You are offered $1 billion, tax-free, with no strings attached. In order to earn the money, you must select an innocent, 4-year-old child from a local daycare, and beat the child to death with a wrench. You will not be prosecuted for the crime, and will face no civil or legal repercussions. Nobody will ever know how you earned your fortune. Would you accept this trade?

5.

On your deathbed, scientists approach you with an intriguing offer. They have the ability to transfer your entire consciousness into a random chimpanzee in the wilds of Africa. Your mind will be teleported into this chimp's brain, in the middle of nowhere, with no humans around for hundreds of miles. You will possess all of your mental faculties within this chimp's body, but you will still lack the vocal-chord configuration required to speak human language. Assume that you do not know sign language and have no way of teaching yourself sign language in the middle of the jungle. Furthermore, assume you do not possess the chimp's instincts or knowledge of its surroundings (its entire mind has been replaced with yours). Would you do it?

6.

A Kryptonian magician offers you all of the powers of Superman. The catch is that, every time use a specific power (flight, x-ray vision, etc.), a random person within a 100-mile radius of you will die. (You will never be one of the possible dead, but your friends and family could be). Do you accept the gift?