Puzzle/logic question

[DayLaPaul]

So much discussion for a thread where the correct answer was given in the 3rd reply.

 

[chuckywang]

Originally posted by: CoinOperatedBoy

Originally posted by: Mo0o
Can the OP just post the answer so we can end this nonsense.

OP doesn't know.

The correct answer is 51/70, the solution was posted several times above.

 

[chuckywang]

Originally posted by: DayLaPaul
So much discussion for a thread where the correct answer was given in the 3rd reply.

The correct answer was given in the 5th reply (mine )

 

[Schfifty Five]

Originally posted by: Mo0o

Originally posted by: Chiropteran

Originally posted by: Mo0o

Originally posted by: Chiropteran

Originally posted by: TallBill

But we're not picking the trick coin. We're checking the odds given the fact that 4 flips have already come up heads, which drives up the odds of the trick coin already being selected. Hence, Bayes theorem.

The odds of any coin giving you heads 4 times in a row is 100%, because it is stated in the puzzle. There is zero chance of getting tails.

please read my comment

I did, the problem with your comment is that it makes no logical sense.

If I pick a coin at random, occasionally picked a coin that flips heads & tails, and occasionally that coin flips heads 1000000/1000000, yes I would assume the one flipping heads all the time was the trick coin.

But if I picked a coin at random multiple times, and EVERY TIME it flipped heads 1000000/1000000, and I knew only one coin was a trick coin? Well I wouldn't know what to think, because the results would be totally illogical. If I am picking a coin at random I should only get the trick coin 5% of the time.



Let me try an analogy.

You have a 6 sided die.

You roll the die 100 times, recording each number. If you roll a 6 at any time during these 100 rolls, you start over and throw away your previous results, until you successfully roll the die 100 times without ever rolling a 6.

What is the chance of recording only numbers one through five with no sixes at all?


Now do the same thing, with a trick die, that has the numbers 1-5 and the 6th face just says "roll again".

Whats the chance of recording only the numbers one through five using the trick die?

Now lets repeat the process, except you pick one of the dice at random, either the real one or the trick one. Same as before, if you roll a 6 you start over.

Now, looking at your list of results, which in either case is going to contain 0 sixes, can you tell which die was used?

Ugh christ I dont even know what to say to you now. You're inventing random rules.

The problem says you pick ONE coin from the pile and flipped it 4 times which came up heads everytime. And now you're about to flip it a 5th time. THAT'S IT.

The results of your last 4 flips matter!! The more times the problem told you you flipped heads, the more likely you have inadvertently picked the trick coin and not a normal coin.

If the problem said you pick a random coin and flipped it a million times and it came up heads everytime, even you would intuitively see the chance of u getting a head on the next flip is higher than 52.5% because the probability of you having selected teh trick coin is much higher than 1/20. So it stands to reason that the # of heads you accomplished (as stated by the problem) matters in the probability result.


Can the OP just post the answer so we can end this nonsense.

This post explains it most clearly.

The only part I see slightly wrong is the bolded.

As the # of consecutive head flips grows larger, the POSSIBILITY of you holding the trick coin goes up, NOT the probability.

The probability of you selecting the trick coin is always 1/20.

I may be wrong on the semantics though.

edit: hmm, the more I think about it, I guess what Mooo had is right as well. The probability of picking the trick coin is 5%, but as you flip more and more consecutive heads, it's more and more probable that you are holding the trick coin. Regardless of the semantics, he still has the right logic/explanation imo.

 

[CoinOperatedBoy]

Originally posted by: Schfifty Five
edit: hmm, the more I think about it, I guess what Mooo had is right as well. The probability of picking the trick coin is 5%, but as you flip more and more consecutive heads, it's more and more probable that you are holding the trick coin. Regardless of the semantics, he still has the right logic/explanation imo.

Yes, it's still just conditional probability. As the number of heads in a row approaches infinity, the probability that you chose the trick coin approaches 1 and the probability that the next flip will be heads also approaches 1.

 

[Praxis1452]

hmm, I was wrong, but I expected that. I admit it. Unlike many in these threads.

 

[DrPizza]

KoolAidKid seems to have posted the correct response first.

For the people who still don't quite "get it" why the first few flips matter, here's a simpler problem:
2 coins. One is heads on both sides, one is tails on both sides. Pick a coin at random and the probability of a heads after 1 flip is 50%

However, if you flip the coin 3 times in a row, and it's heads each time, only a great moron would believe that those flips don't increase the probability (to 100%) that you have the heads on both sides coin, and would insist that the probability on the next flip is still 50%.

Now, for the 20 coin problem, suppose the question was this: determine which coin was heads on both sides. You can only observe one side of the coin after flipping the coin. The first coin, you flip 50 times. 24 times, it comes up heads, 26 times, it comes up tails. You experiment like this for 12 of the coins - the rule you set ahead of time is to flip it 50 times (of course, after the first tails, you can rule out the coin, but you continue to 50 flips anyway.) Now, on the 13th coin, you flip the coin 50 times. It comes up heads 50 times. Do you know 100% for certain that you have the heads on both sides coin? No. But, you can be pretty fricken certain. At this point, hopefully you are not going to continue the argument that on the 13th coin, you know it's one of 8 possible coins that are heads on both sides (because you eliminated 12 of the coins), and that if you flipped it a 51st time, the probability of heads is only slightly better than 50%.

 

[Engineer]

I now understand the solution, but the problem (as it usually is for me) was fully understanding what the OP was asking (i.e. flipping the same coin 5 times in a row and not selecting a different coin each time).

Edit: Well, I understand it enough not to question it...I'm couldn't do it tomorrow without looking at this thread!

 

[CoinOperatedBoy]

Originally posted by: DrPizza
KoolAidKid seems to have posted the correct response first.

ChuckyWang's answer is the same, and posted earlier, but I'm not sure I understand his rationale.

Edit: Removed my boneheaded response to DrPizza's example. I misread.

 

[Engineer]

Originally posted by: CoinOperatedBoy

Originally posted by: DrPizza
KoolAidKid seems to have posted the correct response first.

ChuckyWang's answer is the same, and posted earlier, but I'm not sure I understand his rationale.

For the people who still don't quite "get it" why the first few flips matter, here's a simpler problem:
2 coins. One is heads on both sides, one is tails on both sides. Pick a coin at random and the probability of a heads after 1 flip is 50%

What? No it's not. The probability of heads from a single flip is 75% in your example.

Why? One coin has two heads and one has two tails. The probability of picking the one with two heads is 50% so the chance of getting heads after a flip would be the same as picking the coin with two heads.

 

[CoinOperatedBoy]

Edit: Yeah, I'm an idiot. I didn't realize one coin was two tails in his example.

 

[TallBill]

Edited to avoid spreading the failbug

 

[Engineer]

Originally posted by: CoinOperatedBoy

Originally posted by: Engineer

Originally posted by: CoinOperatedBoy

Originally posted by: DrPizza
KoolAidKid seems to have posted the correct response first.

ChuckyWang's answer is the same, and posted earlier, but I'm not sure I understand his rationale.

For the people who still don't quite "get it" why the first few flips matter, here's a simpler problem:
2 coins. One is heads on both sides, one is tails on both sides. Pick a coin at random and the probability of a heads after 1 flip is 50%

What? No it's not. The probability of heads from a single flip is 75% in your example.

Why? One coin has two heads and one has two tails. The probability of picking the one with two heads is 50% so the chance of getting heads after a flip would be the same as picking the coin with two heads.

Three out of the four coin sides are heads. If you randomly choose a coin and flip it, you have 3/4 chance to get a result of heads.

P(choose trick coin) = 0.5
P(choose normal coin) = 0.5
P(trick coin will flip heads) = 1
P(normal coin will flip heads) = 0.5

P(randomly chosen coin will flip heads) = P(choose trick coin) * P(trick coin will flip heads) + P(choose normal coin) * P(normal coin will flip heads) = (0.5)(1) + (0.5)(0.5) = 0.5 + 0.25 = 0.75

I bolded it for you the first time but re-read what DrPizza posted!

That damn DrPizza is a twicky wascal! :Q

 

[CoinOperatedBoy]

Originally posted by: TallBill

Originally posted by: CoinOperatedBoy

Three out of the four coin sides are heads. If you randomly choose a coin and flip it, you have 3/4 chance to get a result of heads.

P(choose trick coin) = 0.5
P(choose normal coin) = 0.5
P(trick coin will flip heads) = 1
P(normal coin will flip heads) = 0.5

P(randomly chosen coin will flip heads) = P(choose trick coin) * P(trick coin will flip heads) + P(choose normal coin) * P(normal coin will flip heads) = (0.5)(1) + (0.5)(0.5) = 0.5 + 0.25 = 0.75

Fail. 2 out of 4 are heads. Re-read the example, and now you've further cluttered this thread with failure.

Considering nobody else actually explained in detail the calculation to explain the answer to OP's question, I think my fail/win ratio in the thread is still pretty solid. Edited my two prior posts to avoid spreading confusion.

 

[The-Noid]

Better question would be what is the probability that you never flip a heads. Correct answer is 3:1. 3 Chances for heads, 1 chance for tails.

 

[CoinOperatedBoy]

Originally posted by: Yoxxy
Better question would be what is the probability that you never flip a heads. Correct answer is 3:1. 3 Chances for heads, 1 chance for tails.

No, again... don't latch onto my stupid response to DrPizza's scenario. He was actually suggesting that one coin is heads on both sides, while the other is tails on both sides -- not that only one is a trick coin. The other posters are correct that 50% is the probability of getting heads (or tails) in a single random flip. Subsequent flips of the same coin are then 100% certain to produce the same result because after one flip you can be sure which coin you chose.

This is getting away from the OP's question, which has been asked and answered.

 

[Chiropteran]

Originally posted by: GodlessAstronomer

Originally posted by: Chiropteran
Do you see the difference been my revised wording and the OP?

OP:

jar with 20 coins: One of the coins is a trick coin that has both sides heads. You pick a random coin from the jar and flip it 4 times, and each time it comes up heads. What are the chances that the next flip will come up heads?

Your ideal:

A jar has 20 coins, 19 are normal and one has heads on both sides. You pick a random coin from the jar and flip it 4 times. If it came up as heads four times in a row, what are the chances that the next flip will come up heads?

They're nearly identical, what is it you didn't like about the OP wording?

Huge difference.

The OP implies that the coin just happens to come up as heads, which disregards chance. Normally, there is a chance that you will pick a non-trick coin and a chance it will flip as tails. The OP implies that this is impossible, and instead implies that no matter which coin you pick up it's going to flip heads 4 times in a row.

Originally posted by: GodlessAstronomer

Originally posted by: Mo0o

Thats not what the OP's question stated at all.

I think he might just be trolling now. You can't just completely rewrite the question

You don't see the similarity? It's the exact same thing. The only difference is my wording is possible to perform in reality, the OP's question is illogical and impossible.

 

[CoinOperatedBoy]

Originally posted by: Chiropteran
The OP implies that the coin just happens to come up as heads, which disregards chance. Normally, there is a chance that you will pick a non-trick coin and a chance it will flip as tails. The OP implies that this is impossible, and instead implies that no matter which coin you pick up it's going to flip heads 4 times in a row.

There is no such implication in the OP. It's simply providing you with a given scenario and asking you to find a conclusion. The intended meaning is the same as your revised version.

Ass burgers?

 

[Chiropteran]

Originally posted by: CoinOperatedBoy

Originally posted by: Chiropteran
The OP implies that the coin just happens to come up as heads, which disregards chance. Normally, there is a chance that you will pick a non-trick coin and a chance it will flip as tails. The OP implies that this is impossible, and instead implies that no matter which coin you pick up it's going to flip heads 4 times in a row.

There is no such implication in the OP. It's simply providing you with a given scenario and asking you to find a conclusion. The intended meaning is the same as your revised version.

It's not though. A real puzzle should be repeatable and make sense.

One of the coins is a trick coin that has both sides heads. You pick a random coin from the jar and flip it 4 times, and each time it comes up heads. What are the chances that the next flip will come up heads?

Repeat 20 times, until all the coins are taken. Disregarding the absurdity of flipping heads 4 times in a row every single time, look at the average chance that the 5th flip in each case will be heads. Obviously the answer is now different from the "correct" one. How many logical puzzles have a different answer when they are repeated?

 

[CoinOperatedBoy]

Originally posted by: Chiropteran

Originally posted by: CoinOperatedBoy

Originally posted by: Chiropteran
The OP implies that the coin just happens to come up as heads, which disregards chance. Normally, there is a chance that you will pick a non-trick coin and a chance it will flip as tails. The OP implies that this is impossible, and instead implies that no matter which coin you pick up it's going to flip heads 4 times in a row.

There is no such implication in the OP. It's simply providing you with a given scenario and asking you to find a conclusion. The intended meaning is the same as your revised version.

It's not though. A real puzzle should be repeatable and make sense.

It's a statistics question hinging on a single possible scenario. It's not implied that this scenario will occur every time you hypothetically choose a coin from the jar. Consider a single, normal coin and this sentence:

"You flip the coin three times and each time it comes up heads."

It's not a prediction of what would happen if you actually take a coin in reality and flip it three times, although it's possible. It's a given assumption on which something else may be hypothetically based.

OP's question is the same, and GodlessAstronomer's program does a good job of reproducing and testing the results.

 

[Born2bwire]

Originally posted by: Chiropteran

Originally posted by: GodlessAstronomer

Originally posted by: Chiropteran
Do you see the difference been my revised wording and the OP?

OP:

jar with 20 coins: One of the coins is a trick coin that has both sides heads. You pick a random coin from the jar and flip it 4 times, and each time it comes up heads. What are the chances that the next flip will come up heads?

Your ideal:

A jar has 20 coins, 19 are normal and one has heads on both sides. You pick a random coin from the jar and flip it 4 times. If it came up as heads four times in a row, what are the chances that the next flip will come up heads?

They're nearly identical, what is it you didn't like about the OP wording?

Huge difference.

The OP implies that the coin just happens to come up as heads, which disregards chance. Normally, there is a chance that you will pick a non-trick coin and a chance it will flip as tails. The OP implies that this is impossible, and instead implies that no matter which coin you pick up it's going to flip heads 4 times in a row.

Originally posted by: GodlessAstronomer

Originally posted by: Mo0o

Thats not what the OP's question stated at all.

I think he might just be trolling now. You can't just completely rewrite the question

You don't see the similarity? It's the exact same thing. The only difference is my wording is possible to perform in reality, the OP's question is illogical and impossible.

Ahahahahahahahahha.

Oh man, can we check to make sure this isn't an alt-account of smackdown?

 

[Chiropteran]

Originally posted by: CoinOperatedBoy
It's a statistics question hinging on a single possible scenario. It's not implied that this scenario will occur every time you hypothetically choose a coin from the jar.

The way I read it, it is implied.

It says you can pick a coin at random, and that coin flips heads 4 times in a row. If it didn't have the "pick a coin at random part", it would make more sense. for example "you are given a particular coin out of the 20". If it was worded like that, then there would be no implication that every coin is going to show the same result. The "at random" part, to me, implies that you could pick *any* coin and it's going to come up as heads 4 times in a row. Which in turn implies that if you repeat the process you can pick each and every coin and every one of them will flip as heads 4 times in a row.

 

[CoinOperatedBoy]

Originally posted by: Chiropteran

Originally posted by: CoinOperatedBoy
It's a statistics question hinging on a single possible scenario. It's not implied that this scenario will occur every time you hypothetically choose a coin from the jar.

The way I read it, it is implied.

It says you can pick a coin at random, and that coin flips heads 4 times in a row. If it didn't have the "pick a coin at random part", it would make more sense. for example "you are given a particular coin out of the 20". If it was worded like that, then there would be no implication that every coin is going to show the same result. The "at random" part, to me, implies that you could pick *any* coin and it's going to come up as heads 4 times in a row. Which in turn implies that if you repeat the process you can pick each and every coin and every one of them will flip as heads 4 times in a row.

If you pick a coin randomly from the jar and flip it four times, there is a finite set of results. Four heads in a row is part of that set, and yes, any coin could possibly produce it. The OP's question means "assume that is the result you achieved and then use that assumption to form a conclusion." There is no implication that flipping a random coin will always achieve this result.

Is this a joke? If you don't understand, leave it at that and avoid statistics like the plague.

 

[Chiropteran]

Originally posted by: CoinOperatedBoy

Is this a joke? If you don't understand, leave it at that and avoid statistics like the plague.

This is not a statistics issue at all, it is a grammar/linguistics issue. And I'm not convinced you are correct

edit

Originally posted by: CoinOperatedBoy
There is no implication that flipping a random coin will always achieve this result.

YES THERE IS. Can't you read?

You pick a random coin from the jar and flip it 4 times, and each time it comes up heads.

The result happens. It doesn't say *if* it comes up heads 4 times, it simply says it comes up as heads.

If it wasn't supposed to imply that the coin will always come up as heads 4 times, it would have been worded like so:


You pick a random coin from the jar and flip it 4 times, and each time it comes up heads or tails.

 

[Born2bwire]

Originally posted by: Chiropteran

Originally posted by: CoinOperatedBoy

Is this a joke? If you don't understand, leave it at that and avoid statistics like the plague.

This is not a statistics issue at all, it is a grammar/linguistics issue. And I'm not convinced you are correct

edit

Originally posted by: CoinOperatedBoy
There is no implication that flipping a random coin will always achieve this result.

YES THERE IS. Can't you read?

You pick a random coin from the jar and flip it 4 times, and each time it comes up heads.

The result happens. It doesn't say *if* it comes up heads 4 times, it simply says it comes up as heads.

If it wasn't supposed to imply that the coin will always come up as heads 4 times, it would have been worded like so:


You pick a random coin from the jar and flip it 4 times, and each time it comes up heads or tails.

Hahahahahahahahahahahha....

Oh God... stop it, you're killing me.