Toss a coin 10 times.

[joinerjohn]

The toss of a coin is always 50/50 as to what side it lands on. No matter how many times you toss it.
If you tossed a coin 30 times and it had landed on tails every time, the 31'st toss, still only has a 50/50 chance of landing on tails.
So in the original question, all 3 combinations are equally likely.

 

[snico]

The toss of a coin is always 50/50 as to what side it lands on. No matter how many times you toss it.
If you tossed a coin 30 times and it had landed on tails every time, the 31'st toss, still only has a 50/50 chance of landing on tails.
So in the original question, all 3 combinations are equally likely.

But his question is statistically?

 

[UriBentMySpoon]

Statistically, all three are just as likely, just as likely as any specific result you would like to name.

 

[doitall]

I dropped a £1 coin and it was on it's edge, wonder what the chances of that are.

 

[sooey]

Of you dropping a pound coin?

 

[jeds]

Tossing ten coins there are 1024 possible outcomes, each of which are equally likely to happen. Therefore it's just as likely you'll get HTHTHTHTHT, or TTTTTTTTTTT, or HHHHHTTTTT, etc. But if you go into Ladbrokes and ask to place a bet on the world coin tossing championships you'll get better odds on ten consecutive heads than you will on any combination containing equal heads and tails.

 

[JohnD]

...because most mugs don't understand, and bet against it

 

[snico]

Any of the combinations is likely, 10 coins is 1024 outcomes.


1 & 3 are more likely to happen SATISTICALLY, they both have a probabilty of 0.50%

I agree with you because there is very less probability of getting HHHHHHHHHH.

It is true because of the probability factor, but some people say that all outcomes are just as likely....not really true. Probability means, how likely it is that some event will happen. Its a bit of a grey area.

 

[JohnD]

....not really true.

Yes it is.

In the HHHHHHHH example, do you really believe that, for example, the chance of the eighth coin coming up H is not 50%?

 

[snico]

....not really true.

Yes it is.

In the HHHHHHHH example, do you really believe that, for example, the chance of the eighth coin coming up H is not 50%?

It is 50% a single flip of the coin, probability does not dictate that in a 'run' of flips. Thats why it is a bit of a grey area.

If you flipped a coin 10 times, there are 1024 possible outcomes. Of these, 1 outcome has 10 heads. Therefore the probability of this is 1/1024 or 0%

The probabilty of 5 heads when flipping 10 coins is 252/1024 or 25%, 1 head is 10/1024 or 1%.

So we know the probability is how 'likely' an event will happen, we can assume it is more likely that you will have a combination of H and T in a run of flips, not all H or all T.

Theoretically they are all as likely, but statistically they are not

 

[JohnD]

ah, you are saying that you consider

HHHHHHHHHH to be one 10/0 combiation

but

HHHHHTTTTT
and
HTTTTHHH
and
HHTTTTTHHH
and
HHHTTTTTHH
etc
to be the same 5/5 combination

but they aren't
they're all single combinations and they all have exactly the same chance as HHHHHHHHHH

 

[snico]

But we are talking about a run of coin flips, not single events.

Probability says one run is more likely than the other, thats a mathematical fact.........so if the definition of 'probability' is correct, then one is more likely than the other.

If we changed it to tossing a coin 5 times, then the possible outcome combination drops from 1024, to just 32...a lot shorter run. So 5 flips, 5 heads will give you a probability of 1/32, or 3%.....5 flips and just 2 heads will give you 10/32 or 31% so it gets more likely with the shorter run.

If that makes sense

 

[JohnD]

one run is more likely than the other, thats a mathematical fact.

No, that's not true.

Coin no. 10 has no knowledge of what the previous 9 coils fell, so coin 10 has a 50/50 chance of coming up heads, just as coins 1, 2, 3 etc do.
HTHTHTHTHT is exactly as likely as HHHHHHHHHH or HHHHHTTTTT

 

[snico]

one run is more likely than the other, thats a mathematical fact.

No, that's not true.

Coin no. 10 has no knowledge of what the previous 9 coils fell, so coin 10 has a 50/50 chance of coming up heads, just as coins 1, 2, 3 etc do.
HTHTHTHTHT is exactly as likely as HHHHHHHHHH or HHHHHTTTTT

But we are talking about a sequence or run of events. Yes each coin is 50/50.....but what is the probability, thats how we work it out.

Flip 10 coins...HHHHHHHHHH is 1/1024
Flip 10 coins...HTHTHTHTHT is 252/1024
Flip 10 coins...HHHHHTTTTT is 252/1024

Flip 1 coin...H is 1/2

So to flip a coin 10 times, with a result of all heads, as a sequence not a single event, is very unlikely.

 

[UriBentMySpoon]

one run is more likely than the other, thats a mathematical fact.

No, that's not true.

Coin no. 10 has no knowledge of what the previous 9 coils fell, so coin 10 has a 50/50 chance of coming up heads, just as coins 1, 2, 3 etc do.
HTHTHTHTHT is exactly as likely as HHHHHHHHHH or HHHHHTTTTT

But we are talking about a sequence or run of events. Yes each coin is 50/50.....but what is the probability, thats how we work it out.

Flip 10 coins...HHHHHHHHHH is 1/1024
Flip 10 coins...HTHTHTHTHT is 252/1024
Flip 10 coins...HHHHHTTTTT is 252/1024

Flip 1 coin...H is 1/2

So to flip a coin 10 times, with a result of all heads, as a sequence not a single event, is very unlikely.

Each of those three sequences are specific sequences so all thre are 1/1024.

The chances of getting 5 heads in a run of 10, there position within that sequences being unimportant, THAT is more likely than any of the sequences mentioned above, but once you state what the position is, then the odds are 1/1024.