Puzzle/logic question

[Mo0o]

Originally posted by: Chiropteran

Originally posted by: Mo0o
I'm not sure why you're getting hung up on that word. It is accurate because it implies you're not selecting a coin. The "random" aspect is there to make it clear the picker has not applied any kind of criteria into the selection of the coin

That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins. Usually in these sort of puzzles random implies equal chance for any of the possible results.

What. On the initial pick itself the chance is 1/20. The only reason the chance of you having picked the trick coin has gone up is because you have flipped it 4 times and came up heads.

But the very first initial act of reaching into the jar and picking up a coin is not skewed.

Ever piece of new information you gather (flipping heads) increases the probability of you having accomplished something that had a fixed probability of 1/20. So there's two probabilities at work here.

 

[GodlessAstronomer]

Originally posted by: Chiropteran
That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins.

wat

 

[thraashman]

Am I the only one that realizes the idiocy of a certain someone arguing in this thread?


I mean, I'm reading his argument as if he were given the following problem and argues as such.

Solve for X If 2x + 4 = 14

The answer can be proven as x=5

But he keeps saying, "Well what if it's not 4. The problem didn't state it right. The problem should say that x only equals 5 only if you add 4 to 2x and then make it equal 14 and that if you don't then x equals something else but I didn't add 4 at first because I didn't know and the problem wasn't clear!"

It's nonsense. Complete and utter nonsense. I'm fairly certain I could teach this to a 6 year old in faster time than it has taken a certain Chiropteran to accept and admit he is wrong and has been since the beginning.

 

[Chiropteran]

Originally posted by: Engineer

Originally posted by: Chiropteran

Originally posted by: Mo0o
I'm not sure why you're getting hung up on that word. It is accurate because it implies you're not selecting a coin. The "random" aspect is there to make it clear the picker has not applied any kind of criteria into the selection of the coin

That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins. Usually in these sort of puzzles random implies equal chance for any of the possible results.

You had better give a good explanation of this one or you're getting a big WTF?

Each coin has a 1/20 chance of being picked for the experiment, period, so you have a 5% chance of picking the trick coin vs 95% chance of picking a regular coin.

Okay three of you all asked the same thing.

This is how it works:

1- picker picks a coin. 5% chance for any given coin to be picked

2- coin is flipped 4 times

a-fake picked. all flips heads. fake kept
b-real coin picked. one or more flips tails. retroactively "unpicked"
c-real coin picked. one or more flips tails. retroactively "unpicked"
d-real coin picked. one or more flips tails. retroactively "unpicked"
e-real coin picked. one or more flips tails. retroactively "unpicked"
f-real coin picked. one or more flips tails. retroactively "unpicked"
g-real coin picked. one or more flips tails. retroactively "unpicked"
h-real coin picked. one or more flips tails. retroactively "unpicked"
.. repeat X18~ total
x-real coin picked. all flips heads. real kept.

So. The ACTUAL chance of picking a real coin is far lower than 5%, and the actual chance of picking the fake coin is much higher than 5%, because the majority of the real coin picks are retroactively reversed because it doesn't flip heads 4 times in a row.

 

[Engineer]

Originally posted by: Chiropteran

Originally posted by: Engineer

Originally posted by: Chiropteran

Originally posted by: Mo0o
I'm not sure why you're getting hung up on that word. It is accurate because it implies you're not selecting a coin. The "random" aspect is there to make it clear the picker has not applied any kind of criteria into the selection of the coin

That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins. Usually in these sort of puzzles random implies equal chance for any of the possible results.

You had better give a good explanation of this one or you're getting a big WTF?

Each coin has a 1/20 chance of being picked for the experiment, period, so you have a 5% chance of picking the trick coin vs 95% chance of picking a regular coin.

Okay three of you all asked the same thing.

This is how it works:

1- picker picks a coin. 5% chance for any given coin to be picked

2- coin is flipped 4 times

a-fake picked. all flips heads. fake kept
b-real coin picked. one or more flips tails. retroactively "unpicked"
c-real coin picked. one or more flips tails. retroactively "unpicked"
d-real coin picked. one or more flips tails. retroactively "unpicked"
e-real coin picked. one or more flips tails. retroactively "unpicked"
f-real coin picked. one or more flips tails. retroactively "unpicked"
g-real coin picked. one or more flips tails. retroactively "unpicked"
h-real coin picked. one or more flips tails. retroactively "unpicked"
.. repeat X18~ total
x-real coin picked. all flips heads. real kept.

So. The ACTUAL chance of picking a real coin is far lower than 5%, and the actual chance of picking the fake coin is much higher than 5%, because the majority of the real coin picks are retroactively reversed because it doesn't flip heads 4 times in a row.

OK...here comes the WTF! :laugh:

On the initial picking of a coin, a real coin has a 95% chance of being chosen (since there are 19 out of 20). There is a 5% chance of choosing the trick coin.

This has nothing to do with the subsequent flipping of the coin, only the initial choosing of the coin from the group of coins.

If you are talking about "after" choosing and getting 4 heads in a row, then yes, it has been shown that the chances of around 72% that the trick coin was chosen (many times in this thread).

This is starting to come to mind.

 

[TallBill]

Originally posted by: Chiropteran

Originally posted by: TallBill
Because you are a fucking moron. There, I said it.

What kind of life do you live that you get so worked up over posts on a forum that you have to make personal attacks?

First of all, I'm not worked up. And it isn't a personal attack, it's simply stating the truth. Trust me, we were all thinking it.

 

[Mo0o]

Originally posted by: Chiropteran

Originally posted by: Engineer

Originally posted by: Chiropteran

Originally posted by: Mo0o
I'm not sure why you're getting hung up on that word. It is accurate because it implies you're not selecting a coin. The "random" aspect is there to make it clear the picker has not applied any kind of criteria into the selection of the coin

That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins. Usually in these sort of puzzles random implies equal chance for any of the possible results.

You had better give a good explanation of this one or you're getting a big WTF?

Each coin has a 1/20 chance of being picked for the experiment, period, so you have a 5% chance of picking the trick coin vs 95% chance of picking a regular coin.

Okay three of you all asked the same thing.

This is how it works:

1- picker picks a coin. 5% chance for any given coin to be picked

2- coin is flipped 4 times

a-fake picked. all flips heads. fake kept
b-real coin picked. one or more flips tails. retroactively "unpicked"
c-real coin picked. one or more flips tails. retroactively "unpicked"
d-real coin picked. one or more flips tails. retroactively "unpicked"
e-real coin picked. one or more flips tails. retroactively "unpicked"
f-real coin picked. one or more flips tails. retroactively "unpicked"
g-real coin picked. one or more flips tails. retroactively "unpicked"
h-real coin picked. one or more flips tails. retroactively "unpicked"
.. repeat X18~ total
x-real coin picked. all flips heads. real kept.

So. The ACTUAL chance of picking a real coin is far lower than 5%, and the actual chance of picking the fake coin is much higher than 5%, because the majority of the real coin picks are retroactively reversed because it doesn't flip heads 4 times in a row.

Yes that is correct. Given abcdefgh. Essenitally, given the information that you have flipped 4 heads in a row, the chance of you having selected the trick coin is much higher than the chance of you having selected a regular coin. BUT. BUT. Prior to flipping the coin, the INITIAL probability of selecting the trick coin is still 1/20. THUS. THUS. The initial selection of teh coin is truly random. What comes afterwards does not negate the randomness of teh selection event.

Lets say you buy a lottery ticket. And you win. After you find out you win, the probability of you being the winner is 100%. But prior to you finding out you won, the chances of you being teh winner is still 1/eleventybillion. Do you follow? The fact that you won doesnt make the chance of you INITIALLY picking the right number any less likely

 

[Chiropteran]

I thought it was simple enough.

You can't pick a coin that doesn't flip heads 4 times in a row.

The fake coin always flips heads 4X, so you can pick it every time.

The real coins flip heads 4X 6.35% of the time. The other 93.65% they flip tails at least once, and can't be picked.

54.679% chance of getting one of the 19 real coins
2.878% chance of getting any given real coin
45.321% chance of getting the fake

 

[Mo0o]

Originally posted by: Chiropteran
I thought it was simple enough.

You can't pick a coin that doesn't flip heads 4 times in a row.

The fake coin always flips heads 4X, so you can pick it every time.

The real coins flip heads 4X 6.35% of the time. The other 93.65% they flip tails at least once, and can't be picked.

54.679% chance of getting one of the 19 real coins
2.878% chance of getting any given real coin
45.321% chance of getting the fake

YEAH but that's AFTER you have flipped it and received that information. The likelihood of you HOLDING ON to a trick coin is much higher.

But in the initial selection process is still random

 

[Mo0o]

God, this could not describe me any better at this moment: http://imgs.xkcd.com/comics/duty_calls.png

 

[thraashman]

Originally posted by: Chiropteran
I thought it was simple enough.

You can't pick a coin that doesn't flip heads 4 times in a row.

The fake coin always flips heads 4X, so you can pick it every time.

The real coins flip heads 4X 6.35% of the time. The other 93.65% they flip tails at least once, and can't be picked.

54.679% chance of getting one of the 19 real coins
2.878% chance of getting any given real coin
45.321% chance of getting the fake

Probability is a pretty well defined and proven mathematical system. The key here is you're trying to assume you're given more data than you are and are inferring what that data might me.

It's like ... if a bank lender is lending a home loan to someone. The thing this lender knows are that this person has a well paying job, good credit, and no debt. So the probability this person will get the home loan is high.

What the lender doesn't know, and can't know, is that this person is going to lose his job in 3 months and rearend a car and get sued and go in debt. This is data that would change the probability of him lending the money. But the lender doesn't know, he can't know this. You can't assume data that isn't supplied to alter the probability of a math problem. That's what we with math, engineering, or science degrees call stupid.

 

[DrPizza]

Originally posted by: Chiropteran

Originally posted by: Mo0o
I'm not sure why you're getting hung up on that word. It is accurate because it implies you're not selecting a coin. The "random" aspect is there to make it clear the picker has not applied any kind of criteria into the selection of the coin

That isn't true at all though. The picker has a much higher chance of picking the trick coin than any of the real coins. Usually in these sort of puzzles random implies equal chance for any of the possible results.

Wow, how prophetic my post above was. Every time you post, you provide even more evidence that either you're a troll, else an idiot.

 

[GodlessAstronomer]

Originally posted by: Chiropteran
I thought it was simple enough.

You can't pick a coin that doesn't flip heads 4 times in a row.

The fake coin always flips heads 4X, so you can pick it every time.

The real coins flip heads 4X 6.35% of the time. The other 93.65% they flip tails at least once, and can't be picked.

54.679% chance of getting one of the 19 real coins
2.878% chance of getting any given real coin
45.321% chance of getting the fake

You're making my brain cells sad. Please take a class in either statistics or combanatorics.

 

[Schfifty Five]

Originally posted by: Chiropteran
I thought it was simple enough.

You can't pick a coin that doesn't flip heads 4 times in a row.

The fake coin always flips heads 4X, so you can pick it every time.

The real coins flip heads 4X 6.35% of the time. The other 93.65% they flip tails at least once, and can't be picked.

54.679% chance of getting one of the 19 real coins
2.878% chance of getting any given real coin
45.321% chance of getting the fake

To be accurate, shouldn't it be 6.25% and 93.75%?

I'm not agreeing w/ your answer, just correcting some wrong %'s.

 

[Chiropteran]

Originally posted by: thraashman
What the lender doesn't know, and can't know, is that this person is going to lose his job in 3 months and rearend a car and get sued and go in debt. This is data that would change the probability of him lending the money. But the lender doesn't know, he can't know this. You can't assume data that isn't supplied to alter the probability of a math problem.

But the data *is* supplied. We are told the coin flips heads 4X. Therefore the statistical probability of picking the fake coin is so much higher.

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

The puzzles says you picked a coin that didn't flip as tails at all. It basically said you picked one of these coins, where these coins are the 6% of the real coins that flipped heads every time, or 100% of the fake coin that always flips heads.

Originally posted by: Schfifty Five

To be accurate, shouldn't it be 6.25% and 93.75%?

Yeah, it was a typo and then I went back and used the typo when I calculated the other number. Thanks for pointing it out.

 

[GodlessAstronomer]

Originally posted by: Chiropteran

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

You're officially a lost cause. You simply don't have the mental acumen to understand simple problems. May I suggest a liberal arts curriculum for you?

 

[Chiropteran]

Originally posted by: GodlessAstronomer

Originally posted by: Chiropteran

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

You're officially a lost cause. You simply don't have the mental acumen to understand simple problems. May I suggest a liberal arts curriculum for you?

Pick a card at random, any card. If it's not the 4 of diamonds put it back and pick another card at random, repeat until you get the 4 of diamonds.

Whats the chance of picking the 4 of diamonds? 1/52 because you picked it out of 52 cards, AMIRITE?

Obviously not. Which is why the chance of picking the fake coin is far higher than 1/20, because most of the real coins you pick are put back and picked again.

 

[Mo0o]

Originally posted by: Chiropteran

Originally posted by: thraashman
What the lender doesn't know, and can't know, is that this person is going to lose his job in 3 months and rearend a car and get sued and go in debt. This is data that would change the probability of him lending the money. But the lender doesn't know, he can't know this. You can't assume data that isn't supplied to alter the probability of a math problem.

But the data *is* supplied. We are told the coin flips heads 4X. Therefore the statistical probability of picking the fake coin is so much higher.

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

The puzzles says you picked a coin that didn't flip as tails at all. It basically said you picked one of these coins, where these coins are the 6% of the real coins that flipped heads every time, or 100% of the fake coin that always flips heads.

Originally posted by: Schfifty Five

To be accurate, shouldn't it be 6.25% and 93.75%?

Yeah, it was a typo and then I went back and used the typo when I calculated the other number. Thanks for pointing it out.

DUDE.

Ok...

The problem states you flipped heads 4 times. You could have easily picked a regular coin and got realy lucky and flipped it heads 4 times. Its unlikely but possible.

At the end of the problem, as you are about to flip the coin a 5th time, the probabliilty of you having picked a trick coin is much higher than 1/20. We all agree.

But prior to flipping the coin. So at this part of the problem "One of the coins is a trick coin that has both sides heads. You pick a random coin from the jar..." the chance of you holding on to a trick coin is only 1/20. Then as you keep flipping heads (as stated by teh problem), the probability of you holding on to a trick coin keeps going up. BUt the intial selection (prior to all teh flips), the chance of u grabbing the trick coin is still 1/20.

The problem isnt implying that everytime you reach in and start flipping teh coin, you'll get 4 heads in a row. What its saying is, THIS ONE SERIES, you picked a coin, flipped 4 times and got all heads. And ask you to calculate some probabilities. Thats it. So this series could be a very unlikely series of events that has occured.

 

[Engineer]

Originally posted by: Chiropteran
If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

It didn't say that you can't pick one, it stated that you didn't pick one. By chance, whatever percentage that is, the coin that was chosen hit heads on the first 4 flips. What is the chance that it does it on the next flip (#5)?

Because the coin just so happened to flip the first 4 times as heads, the probability that it is indeed the trick coin increases but it does not mean that it wasn't a regular coin on the initial choosing. Each regular coin had a 5% chance of being picked and the trick coin had a 5% chance of being picked (initially on both). 95% chance that a regular coin was chosen at the beginning.

Nowhere did it state what coin was picked or that the coin that you picked HAD to hit heads 4 consecutive times, it just did (by whatever chance it had).

How hard is this to understand?

 

[Mo0o]

Originally posted by: Chiropteran

Originally posted by: GodlessAstronomer

Originally posted by: Chiropteran

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

You're officially a lost cause. You simply don't have the mental acumen to understand simple problems. May I suggest a liberal arts curriculum for you?

Pick a card at random, any card. If it's not the 4 of diamonds put it back and pick another card at random, repeat until you get the 4 of diamonds.

Whats the chance of picking the 4 of diamonds? 1/52 because you picked it out of 52 cards, AMIRITE?

Obviously not. Which is why the chance of picking the fake coin is far higher than 1/20, because most of the real coins you pick are put back and picked again.

NO. THERE IS NO PUTTING BACK.

You picked up one coin, and by sheer luck you managed to get 4 heads. Whether that luck was because you picked a regular coin and landed 4 heads or by the luck of you picking teh trick coin and guaranteeing 4 heads... thats all calculated into the math.

If the problem states: You draw 2 cards from a deck of cards. You drew the Ace of spades and the ace of diamonds. What was the possibility that you drew the ace of spades and ace of diamonds? That probability is 1/52 * 1/51. It implies you managed to accomplish a very unlikely event, not that you kept repeating the process until you managed to meet the conditions of the problem.

 

[thraashman]

Originally posted by: Chiropteran

Originally posted by: GodlessAstronomer

Originally posted by: Chiropteran

Originally posted by: Mo0o

But in the initial selection process is still random

If it was, you could pick a coin that doesn't flip as heads 4X. You can't.

You're officially a lost cause. You simply don't have the mental acumen to understand simple problems. May I suggest a liberal arts curriculum for you?

Pick a card at random, any card. If it's not the 4 of diamonds put it back and pick another card at random, repeat until you get the 4 of diamonds.

Whats the chance of picking the 4 of diamonds? 1/52 because you picked it out of 52 cards, AMIRITE?

Obviously not. Which is why the chance of picking the fake coin is far higher than 1/20, because most of the real coins you pick are put back and picked again.

Here's where you're using data you've not been supplied. All you know is that a coin is picked, flipped 4 times, comes up heads all 4 times. You don't have ANY idea if this coin was picked the first time, or the 400th time a coin was picked.

 

[Chiropteran]

Originally posted by: Engineer


It didn't say that you can't pick one, it stated that you didn't pick one.
...
How hard is this to understand?

That doesn't matter if you can't or didn't, same thing either way.

Look, here is super simple example.

You roll a 6 sided die. You didn't roll a 5.

What is the chance that you rolled a 4?

Is it 1/5, or 1/6?

I think the obvious answer would be 1/5. Given the knowledge that you didn't roll a 5, there are 5 other possible rolls, and the chance of getting any one of them is 1/5.

If you think it's 1/6, explain why. Keep in mind there is no possibility that you rolled a 5.

 

[Mo0o]

Originally posted by: Chiropteran

Originally posted by: Engineer


It didn't say that you can't pick one, it stated that you didn't pick one.
...
How hard is this to understand?

That doesn't matter if you can't or didn't, same thing either way.

Look, here is super simple example.

You roll a 6 sided die. You didn't roll a 5.

What is the chance that you rolled a 4?

Is it 1/5, or 1/6?

I think the obvious answer would be 1/5. Given the knowledge that you didn't roll a 5, there are 5 other possible rolls, and the chance of getting any one of them is 1/5.

If you think it's 1/6, explain why. Keep in mind there is no possibility that you rolled a 5.

Yeah but you're altering the order the information is being provided. On the very intiial roll, the chance of you getting a 4 is 1/6. ONLY after finding out you didnt get a 5, can you probability reach 1/5. So the die is not a trick die that is going to give you a 1/5 probability of rolling a 4. Its only because you are provided information afterwards that you change the probability that you have rolled a 4

 

[Engineer]

Originally posted by: Chiropteran

Originally posted by: Engineer


It didn't say that you can't pick one, it stated that you didn't pick one.
...
How hard is this to understand?

That doesn't matter if you can't or didn't, same thing either way.

Look, here is super simple example.

You roll a 6 sided die. You didn't roll a 5.

What is the chance that you rolled a 4?

Is it 1/5, or 1/6?

I think the obvious answer would be 1/5. Given the knowledge that you didn't roll a 5, there are 5 other possible rolls, and the chance of getting any one of them is 1/5.

If you think it's 1/6, explain why. Keep in mind there is no possibility that you rolled a 5.

No where in the OP did it state that the coin chosen could not land on tails. No where. Just by chance (whether it's 100% from the trick coin or 1/2*1/2*1/2*1/2 from the regular coins), the coin that was chosen flipped 4 consecutive heads. You are given this information as an "after the fact" action, not a "it's always going to land on heads 4 consecutive times no matter how many times you do the experiment" for future experiments.

If the OP had told you that the chosen coin just by chance landed on 4 consecutive heads, would that have made you feel better?

You're being completely OBTUSE (as the video states). I'm (and many others) just shaking my head at this point.

Nor does the given information (after the fact) change the FACT that each regular coin had the INITIAL probability of 5% of being picked as did the trick coin. Since there are 19 regular coins, there is a 95% chance of INITIALLY choosing a regular coin. Given the information that AFTER the chosen coin landed on heads 4 consecutive times, it can be calculated that the probability that the trick coin chosen is higher than 5% (initial), hence the ~72% chance that the next flip will land on heads (calculated by many in this thread).

 

[yuchai]

Originally posted by: Chiropteran

Originally posted by: Engineer


It didn't say that you can't pick one, it stated that you didn't pick one.
...
How hard is this to understand?

That doesn't matter if you can't or didn't, same thing either way.

Look, here is super simple example.

You roll a 6 sided die. You didn't roll a 5.

What is the chance that you rolled a 4?

Is it 1/5, or 1/6?

I think the obvious answer would be 1/5. Given the knowledge that you didn't roll a 5, there are 5 other possible rolls, and the chance of getting any one of them is 1/5.

If you think it's 1/6, explain why. Keep in mind there is no possibility that you rolled a 5.

Your "obvious" answer of 1/5 is analogous to the correct 51/70 answer in the original question. But, for the longest time, you were arguing for 21/40, which is analogous to the 1/6 in your question.

The fact that you stated "you didn't roll a 5" is analogous to the problem stating "you rolled 4 heads". They are hypothetical situations that may or may not occur every time in real life.