A question...

[beam]

Here's my question:

Is it possible to flip a coin repeatedly for an infinite amount of time and have it never land tails?



Don't try to guess where I'm going with this...just discuss the question.

[Foxworthy]

Here's my question:

Is it possible to flip a coin repeatedly for an infinite amount of time and have it never land tails?



Don't try to guess where I'm going with this...just discuss the question.

Sure, if both sides are heads. Though I guess even if one side was tails it would be possible, but it would be so highly improbably that it would never actually happen in a non controlled case.

[pmstc]

Yes, it is possible.

[DevilMan]

Possible YES.... Probable NO...

DM

[acropilot19]

Wow...

...The blond in the banner ad at the top of this page is HOT!
I'm sorry, what was this thread about, I already forgot...

[punkncat]

No

Given that the "probable" chance is (about) 50/50 that it will land on one, the high percentage chance that it will land the other way will come up eventually.

If you are taking about an even less chance, say 99% that it would always land on one or the other, extended over an infinate period of time even that 1% is going to show itslef eventually.

How many women got pregnant on the pill?....

[teufelhunden]

Possible YES.... Probable NO...

DM

Yes. What he said.

[beam]

Is the following logic correct?

Each flip is an individual event. It's outcome is not dependent or influenced by any event that has preceded the current flip.

If I flip it and it lands heads 50 times, that does not mean that it has a greater chance of landing tails on the 51st flip. The chance for the 51st flip is the exact same as it was for the first flip...50-50.

What guarantees that there will ever be a tail in this scenario? And don't get hung up on the purity of the randomness of the flip. Assume each flip is brilliantly and perfectly executed to produce a random result.

[pmstc]

Is the following logic correct?

Each flip is an individual event. It's outcome is not dependent or influenced by any event that has preceded the current flip.

If I flip it and it lands heads 50 times, that does not mean that it has a greater chance of landing tails on the 51st flip. The chance for the 51st flip is the exact same as it was for the first flip...50-50.

What guarantees that there will ever be a tail in this scenario? And don't get hung up on the purity of the randomness of the flip. Assume each flip is brilliantly and perfectly executed to produce a random result.

Each flip is an individual event. This is true. Which is why it is theoretically possible. But, just because each flip is 50-50, doesn't mean that its likely to happen.
If you flip it and it lands heads 50 times, then you have a 50% chance of getting heads the next flip. BUT, the probability of you flipping a coin 51 times and getting heads every time would be ridiculously small. It would reduce by a factor of two every flip, I think.

To every one else: He was not asking if it was probable, just possible. There is no gremlin that lives on the heads side of the coin and makes it flip tails every other time you flip the coin. It is entirely possible.

[punkncat]

The saying goes that ANYTHING is "possible".

But realistically when you stretch out an even chance of an event going either way into infinity, it simply is not going to happen.


I wonder if this question didn't start here?

http://espse.educ.psu.edu/edpsych/faculty/rhale/statistics/Chapters/Chapter7/Chap7.html

and influence from here:

http://espse.educ.psu.edu/edpsych/faculty/rhale/statistics/Chapters/Chapter7/flipans.html

stating....

If you flipped the coin a sufficient number of times, your found probability will be very close to the expected probability of one half (0.5). The coin you were flipping was programmed to simulate a fair coin. However, it is possible that even with this fair coin that your found probability might be quite a bit different from 0.5. However, this would happen very rarely. Or using statistical language: the probability that your found probability is very different from 0.5 is quite low given this fair coin.

???

[jenarelJAM]

Here's an idea!

Fact 1:
If one flips a theorhetical quarter, with an equal chance it will land heads or tails, 1/2 of the time it will land on heads. If it is flipped again, the chance it will lands on heads is still 1/2.

Fact 2:
If each time it flipped, it has a 1/2 chance, so the chance of it being flipped heads twice in a row would be 1/4 chance, three times would be 1/8 chance, and so on.

Fact 3:
If this process is repeated indefinitely, the infinite geometric series (1/2)^n is formed, where n is the number of times it has been flipped, and the entire expression is the chance of heads being flipped n consecutive times.

Fact 4:
The limit as n approaches infinity of (1/2)^n is zero.

Disclaimer: This is food for thought. Yes it's possible, but improbable to an extreme.

[beam]

Here's an idea!

Fact 1:
If one flips a theorhetical quarter, with an equal chance it will land heads or tails, 1/2 of the time it will land on heads. If it is flipped again, the chance it will lands on heads is still 1/2.

Fact 2:
If each time it flipped, it has a 1/2 chance, so the chance of it being flipped heads twice in a row would be 1/4 chance, three times would be 1/8 chance, and so on.

Fact 3:
If this process is repeated indefinitely, the infinite geometric series (1/2)^n is formed, where n is the number of times it has been flipped, and the entire expression is the chance of heads being flipped n consecutive times.

Fact 4:
The limit as n approaches infinity of (1/2)^n is zero.

Disclaimer: This is food for thought. Yes it's possible, but improbable to an extreme.

Here's another idea.

Start flipping. It lands heads time after time after time. This is theoretically possible...but as some have said not likely. This outcome is deemed a failure as soon as a tails is flipped.

BUT...we are flipping for infinity, so we can always start over and once we get another good string of heads going...we can assume that if I do this for infinity, that eventually I will get into a string of heads only that tails will never again land.

Make sense?

[Lohman446]

As has been stated before each flip is an independent act totally independent of the results from the time before (assuming a perfect coin / flip)

Thus, if the flip before this flip was heads, this one is still a fifty fifty chance of being heads.

If the 999 flips before this flip were all heads, this one is still a 50/50 chance of being heads.

So each individual flip has a 50/50 chance.

Don't get hung up on the other side of the argument too much. The chances of flipping two heads in a row (not individual events) are 1/4 (1/2 X 1/2). The chances of flipping three heads in a row are 1/8. While this is true that the odds get closer to 1/1 they never will actually hit it so you are never guarenteed to flip a tail.

The counterexample is blackjack, and counting cards more speficially. To simplify things we are going to assume one legal deck. Without getting into the specifics of counting the base strategy (of positive and negative numbers) is based on the likelihood of high value cards coming up. Because the cards are in a shoe on the table the odds of the next hand are dependent on the odds of the hand before.

Say I have one deck, the odds of drawing the Ace of hearts on the first card are 1/52. The second 1/51, the third 1/50 and so on down the line. Because these are dependent on the draw before you slowly reach come down to 1/1 (you will draw it within 52 draws).

Coin flips - independent events. Drawing cards out of a deck (assuming you are leaving the cards drawn out) are dependent events.

[Army]

Of course, the odds are really 49% to 49%, with 2% possibility of it landing, and staying, on the edge

[drg]

I belive it is not possible due to the fact that you are doing it infinitely. You can't ever say for sure that it 'never' landed tails. Because ... flip again.