Two coin trick

[En_Route]

Two coins  each with a head one one side and a tail on the other  are tossed in the air but you do not see them land.
You are told that one of the coins landed showing heads. What are the chances that the other coin also landed showing heads?

[Asmodean]

25%

[Stevil]

25%

That's not right.

[Ecurb Noselrub]

Isn't it still 50-50?  What side the one coin landed on has nothing to do with the other coin.  I'm not real confident about this, as you can see.

[Ali]

Two coins  each with a head one one side and a tail on the other  are tossed in the air but you do not see them land.
You are told that one of the coins landed showing heads. What are the chances that the other coin also landed showing heads?

You again!?!

[Stevil]

Isn't it still 50-50?  What side the one coin landed on has nothing to do with the other coin.  I'm not real confident about this, as you can see.

Don't be lazy people, you assume too much, do the permutations, there are only 4 of them.

[Jimmy]

1/2*1/2= 1/4

[Stevil]

P1 - H, T
P2 - T, H
P3 - T, T
P4 - H, H

P1,2,4 all have one coin with H
With the other coin being H once or T twice
So 1/3 = 33.333%

[Jimmy]

seems the trick can be with the wording, perhaps I'm not interpreting it the same way.....

the probably that it will "also land on heads", implies  "and," so the probability that it is heads is just a simple probability calculation, which is 50% heads each flip, which is just 25% for HH

HH, HT, TH, TT all have an equal chance of occurring.

Although, perhaps because the first heads is known already, the probability of the second coin landing on heads is independent of the first toss, and therefore,  50%

I can't fathom anything other than 50% or 25%, the 33.33%; just does not compute without a further explanation.

[Stevil]

seems the trick can be with the wording, perhaps I'm not interpreting it the same way.....

the probably that it will "also land on heads", implies  "and," so the probability that it is heads is just a simple probability calculation, which is 50% heads each flip, which is just 25% for HH

HH, HT, TH, TT all have an equal chance of occurring.

Although, perhaps because the first heads is known already, the probability of the second coin landing on heads is independent of the first toss, and therefore,  50%

I can't fathom anything other than 50% or 25%, the 33.33%; just does not compute without a further explanation.

The original question states
"also landed showing heads?"
This is past tense.
So both coins have already landed.
A person has told you that one of them was heads.

There are 4 possible permutations but only 3 that contain at least one head.
So we only have 3 possible permutations.
Of those only one contains another head. The HH permutation.
The other two perms are HT and TH.
So chances of a second heads, given that one of the coins is known as heads is 1/3 = 33.333%

I think the question is stated very clearly.

[Jimmy]

seems the trick can be with the wording, perhaps I'm not interpreting it the same way.....

the probably that it will "also land on heads", implies  "and," so the probability that it is heads is just a simple probability calculation, which is 50% heads each flip, which is just 25% for HH

HH, HT, TH, TT all have an equal chance of occurring.

Although, perhaps because the first heads is known already, the probability of the second coin landing on heads is independent of the first toss, and therefore,  50%

I can't fathom anything other than 50% or 25%, the 33.33%; just does not compute without a further explanation.

Scratch that, I got it......wording....TT rule out only leaves three options, 1/3H to 2/3 T on second toss

I

[OldGit]

50-50.  Neither coin is in any way affected by the fall of the other.

[The Magic Pudding]

50-50.  Neither coin is in any way affected by the fall of the other.

If he'd told you one was heads before the other had been tossed it would be 50-50
But he hasn't, you've been given enough information to conlude the fall is head/head, head/tail or tail/head, there's three opions.  It's the devil's 66.6% thing again, well 33.3% this time but same devilish principle.

[En_Route]

seems the trick can be with the wording, perhaps I'm not interpreting it the same way.....

the probably that it will "also land on heads", implies  "and," so the probability that it is heads is just a simple probability calculation, which is 50% heads each flip, which is just 25% for HH

HH, HT, TH, TT all have an equal chance of occurring.

Although, perhaps because the first heads is known already, the probability of the second coin landing on heads is independent of the first toss, and therefore,  50%

I can't fathom anything other than 50% or 25%, the 33.33%; just does not compute without a further explanation.

The original question states
"also landed showing heads?"
This is past tense.
So both coins have already landed.
A person has told you that one of them was heads.

There are 4 possible permutations but only 3 that contain at least one head.
So we only have 3 possible permutations.
Of those only one contains another head. The HH permutation.
The other two perms are HT and TH.
So chances of a second heads, given that one of the coins is known as heads is 1/3 = 33.333%

I think the question is stated very clearly.

The solution (as per your lucid exposition) is relatively evident to those with a stats background but counter-intuitive to those not initiated into those dark arts. The research suggests that the human brain is not wired in such away as to have an instinctive grasp of probability- rather the reverse.

[xSilverPhinx]

seems the trick can be with the wording, perhaps I'm not interpreting it the same way.....

the probably that it will "also land on heads", implies  "and," so the probability that it is heads is just a simple probability calculation, which is 50% heads each flip, which is just 25% for HH

HH, HT, TH, TT all have an equal chance of occurring.

Although, perhaps because the first heads is known already, the probability of the second coin landing on heads is independent of the first toss, and therefore,  50%

I can't fathom anything other than 50% or 25%, the 33.33%; just does not compute without a further explanation.

The original question states
"also landed showing heads?"
This is past tense.
So both coins have already landed.
A person has told you that one of them was heads.

There are 4 possible permutations but only 3 that contain at least one head.
So we only have 3 possible permutations.
Of those only one contains another head. The HH permutation.
The other two perms are HT and TH.
So chances of a second heads, given that one of the coins is known as heads is 1/3 = 33.333%

I think the question is stated very clearly.

The solution (as per your lucid exposition) is relatively evident to those with a stats background but counter-intuitive to those not initiated into those dark arts. The research suggests that the human brain is not wired in such away as to have an instinctive grasp of probability- rather the reverse.

For certain