Two Coins: Probability

nashy19

nashy19

Nashy (as himself)
mjbabl.jpg


That's the question.

My thoughts:
[spoil]There's four possible results: TH, HT, HH and TT. Ignoring the TT because one coin has to be heads there's 3 which makes it 1/3. However I'm not sure whether TT should just be ignored, because there is a 50% chance one coin is tails, in which case the next coin must be heads.[/spoil]
 
Last edited:

DeletedUser

The answer is 50%

If you know one is heads, then the question pertains only to the status of the unknown coin. I.e., heads or tails.

Of course, you can get even trickier and give precise examination of wieght distribution, wear, surface, whether there was any influence, posed by the coin tosser, to the variability of the toss itself, etc and so on.
 
nashy19

nashy19

Nashy (as himself)
Hellstromm said:
If you know one is heads, then the question pertains only to the status of the unknown coin. I.e., heads or tails.
Click to expand...

But if the flip of that single coin (50% each side) is heads, then the other coin isn't certain to be heads.
 

DeletedUser

it's 25% when both coins are uncertain and 50% if one coin is certainly heads
 

DeletedUser

Who is that in the picture? I feel she has something to do with the probability......
btw, does quantum mechanics or general relativity apply? because that makes a big difference.
 

DeletedUser

nashy19 said:
My thoughts:
There's four possible results: TH, HT, HH and TT. Ignoring the TT because one coin has to be heads there's 3 which makes it 1/3. However I'm not sure whether TT should just be ignored, because there is a 50% chance one coin is tails, in which case the next coin must be heads.
Click to expand...
Your problem lies here: TH=HT, so one of them should be ignored also. That leaves you with two possibilities: TH & HH, ergo a 50% chance.
 
Last edited by a moderator:

DeletedUser

The probablility that both are heads, knowing that at least one is, is one-third.

There are 4 possible combinations, all equally probable:

1. Tail, Tail
2. Tail, Head
3. Head, Tail
4. Head, Head

So, knowing that at least one coin is heads eliminates possibility 1.
Of the 3 remaining possibilities only one is a double-head, so the possibility of both coins being heads is one in three.

That is the mathematics of probability. There's no point in further discussion - that is the answer.
 

DeletedUser28032

(Cat...Check, Flock of Pigeons....Check...Ok here goes)

What about the mathmatically small chance that the coin will land on its edge? therefore being neither heads nor tails
 

DeletedUser

I agree with Hellstromm. If you know that one is heads, the chances of the other being heads would be the same as if you only flipped one coin. It can be heads or it can be tails.
 

DeletedUser9470

Eli Makepeace said:
The probablility that both are heads, knowing that at least one is, is one-third.

There are 4 possible combinations, all equally probable:

1. Tail, Tail
2. Tail, Head
3. Head, Tail
4. Head, Head

So, knowing that at least one coin is heads eliminates possibility 1.
Of the 3 remaining possibilities only one is a double-head, so the possibility of both coins being heads is one in three.

That is the mathematics of probability. There's no point in further discussion - that is the answer.
Click to expand...

correct.
In maths this is indisputable.
However irl, I like what braetwalda points out.
What are the possibilities of the coins never landing at all?
 

DeletedUser16008

nashy19 said:
mjbabl.jpg


That's the question.
Click to expand...

Look again Eli & Neo

No one required a working out of 4 different outcomes one coin has been done for you thus taking half of the possible outcome away.

According to the question and information above ... There is only required the possibility of a heads or tails with the second coin as Artemis just said

The answer is still 50%.
 

DeletedUser9470

You are assuming that the coins are flipped successively, thus after landing one head what are the odds that the next flip lands head?

yet as posed in this problem, there is only one event.

"you flip 2 coins"
consider that you cannot see both coins, they are tossed together and hidden from you.
you are then told that at least 1 is heads...

you dont know if it is coin 1 or coin 2 that is the one designated by "at least one is heads".

the answer is definitely 1/3

There are 4 possible outcomes when tossing 2 coins.
If you know that at least one is heads then you can rule out the tails/tails outcome.
which leaves you with 3 possible outcomes.

there is only 1 event with 2 variables.
not 2 events...
 

DeletedUser

As said before, since one coin's result is already certain the probability is entirely about the other coin. To illustrate:

In total there are four results for tossing two coins: HH, HT, TH, TT.
However, since HT and TH are basically the same result, one of them is eliminated, leaving HH, HT, and TT.
Of course, TT is an impossibility in this case, so that leaves us with two results, HH and HT.

Therefore, a 50% chance.
 

DeletedUser

If you flipped coin A and coin B, and one of them landed on heads, the odds would be 1:3 that coin A (or coin B) was heads. The odds that the second coin is heads (not specifying which coin it is) would be 1:2. Is that confusing enough? :huh:
 

DeletedUser

Hehe, I guess we'll continue.

It's all in the phrasing of the question. It is not asking what the chances are that two coins are tossed, resulting in both being heads and ignoring any toss that is both being tails. It indicates that one of them is heads. Knowing that one of them is heads leaves you only speculating the status of the "other" coin. I.e., 50% chance.
 
Last edited by a moderator:

DeletedUser9470

Indeed, its phraseology, basic comprehension of English.

It didn't say that the first was heads, it said at least one was heads. There are indeed three equally-likely ways to get "at least one" with heads,
and only one of these has two heads.
This is NOT the same as the following question:
If I have a coin that is heads, what is the chance of flipping another coin and having two heads?

To help you I have worded the question differently
The question posed is this: What is the chance of having two heads (HH) if I tell you that the outcome is NOT two tails (TT)?
[This is the EXACT same question as the teaser, worded differently]
1 - HH
2 - HT
3 - TH
4 - HH

The main point of confusion here is the fact that HT and TH are NOT equal. These are two distinct events, even though they appear the same
to help you understand these are completely different events consider these questions:
What is the chance of getting HH?
1/2 x 1/2 = 1/4
What is the chance of getting TT?
1/2 x 1/2 = 1/4
What is the chance of getting one heads and one tails? This is just 100% - 25% - 25% (from above)
1 - 1/4 - 1/4 = 1/2.
As you can see, you are twice as likely to get heads and tails combined, because there are two ways to accomplish it.

out of the 4 possible combinations only 3 are left
the answer is 1/3
What's the probablilty of everyone getting their heads around this? Very slim
:tumble:
 
Last edited by a moderator:
Slygoxx

Slygoxx

Well-Known Member
HT and TH are equal.

You have at least one heads, you do not know whether it is the first or the second coin you flip.
If you have the HT combination, the first coin you flip is heads, the second is tails. If you have the HT combination, it's the other way around. What you end up with is 1 heads, and 1 tails, in both situations. Therefore making them equal for this particular question.

If you flip a coin and it's tails, you will know the next one will be heads.
If you flip a coin and it's heads, you have a 50% chance that the next one will be heads.
 
Last edited:
You must log in or register to reply here.
Top