You have a 50/50 chance of getting the two headed coin. After you pull it out it doesn`t matter what is showing, it`s still 50/50 it will be heads on the other side.

It`s not 50/50 - that would be the chance of holding either one of the coins. However, when the question is asked, we are already looking at one (out of three) head sides. Two of them have another head on their back, one does not. That makes it 2/3 for getting another head.

The question is better asked, "If you pull a coin showing heads, what are the odds that it is the double sided coin." The answer to that is clearly 50/50. It doesn`t matter which side of the double sided coin is up. You still have a 50/50 chance of having pulled it. Therefore, you have a 50/50 chance of the other side being heads as well (either you pulled the double side coin, and the other side is heads, or you pulled the normal coin and the other side is tails).

There`s a 75% chance that the coin you select will show heads. Therefore, there are 3 remaining possibilities for the other side of the coin that you did select: 1) side B of the regular coin (tails); 2) side A of the two-headed coin (heads); or side B of the two-headed coin (heads). Out of those 3 possibilities, the odds are 2/3 that the other side is heads.

Because you initially drew heads, you eliminated one of the 4 possibilities. There are still 2 chances that there is a head on the other side, but that is now 2 out of only 3 remaining possibilities.

Gerry1of1 The side showing does matter on the first coin. 3/4 times heads will show while 1/4 of the times tails will show. But if the first coin shows tails then 1/1 times the other side is heads. The 1/1 math works the same as the 2/3.

I`ve seen this puzzle in a J-Drama, Liar Game, they explained it really well. Using cards instead.

Someone used it as a scam in the show to cheat someone.

As Fwoggie2 said, "It`s the specific wording.

"What`s the probability that the other side ALSO shows heads." "

There are 4 outcomes in this case: Double Coin Heads, Flip Double Coin Heads Double Coin Heads, Flip Double Coin Heads Other Coin Heads, Flip other coin shamrock Shamrock Coin, Flip other coin Heads

Since Shamrock is eliminated right away when you pull it, only the other 3 options count, making it 2/3 chance of being heads.

Original trick with cards: Normal Joker, Double sided back of card. Outcomes as follows:

Double Card Back, Flip Double Card Back Double Card Back, Flip Double Card Back Joker backside, Flip Joker Joker Faceside would call for a redo.

4 outcomes, 50% being backside of a card, 25% Joker, 2

"Hence 50% chance. Either you pulled that coin or you didn`t."

You are drawing sides of a coin, so there are 4 possibilities in the first draw. 1 of them is not considered (drawing tails).

You pull out the coin and see heads. It`s either the 1st side of the double-sided coin, the second side of the double-sided coin, or the heads side of a standard coin. When you flip it over, 2 of the 3 possibilities will reveal heads again.

The question needs to state that your selected coin is showing heads. Then the answer is 2/3. But, although they showed a picture of the coin in your hand showing heads, the question did not actually state that the coin is showing heads, just uses an awkward "also" without clarifying the word "also" refers to in addition to the heads side showing in your hand. They need to state that condition instead of just showing it in a picture

To me, you only have two possible outcomes *if* you draw heads as the initial condition, which is stated. So it confuses the issue, given that you`ve already stated the initial condition is a draw of heads, to say there are four potential combinations. That`s only true if you`ve not already drawn.

Once heads is drawn, there are only two possible outcomes with that given: that you are holding the double-headed coin, thus the other side is heads, *or*, that you`re holding the standard coin and the other side is tails.

Once you`ve drawn heads initially, those are the ONLY two possibilities. So, it`s 50/50 under the given circumstances, IMHO.

There are 2 initial probabilities. I draw the double headed coin, or the shamrock coin.

If I`ve drawn the shamrock coin, the probability of the other side that the other side also shows heads is 0, because either the face I`m looking at is a shamrock, or the other face is the shamrock. This is why the wording is so important - the other side must ALSO a head. This is impossible with the Shamrock coin, regardless of which face you`re looking at.

I`ve I`ve drawn the double headed coin, obviously the other side is a head, so the probability is 1 (100%).

Smagboy "once a heads is drawn there are only two possibilities". This is your mistake in your thinking, the two sides of the same-side coin constitute two distinct events/possibilities, not one. You are either looking at side A of the double-sided coin, side B of the double-sided coin or the heads side of the standard coin. So 2/3 is right.

paperduck - the standard coin cannot be included, because it asks if the other side of the coin is also a head. If you`re holding the standard coin, the other side might be the head, but your side therefore isn`t also a head.

paperduck, I agree with your logic if we`d not already drawn a coin. But, if you`re holding a "heads" value already, in other words if it`s already in your hand and visible, then you`ve eliminated not just one possibility (that you`d draw tails), but, now that it`s in your hand and reading "heads", regardless the coin you have, the chances of the other side being heads are 100% for one coin (the two-headed one) and 0% for the other (the standard coin).

Even if we hadn`t already drawn, the two-headed coin`s two outcomes are exactly equal if you`re looking for heads and only heads (e.g. if that`s your condition), so, as such, landing on heads for that coin is a 100% chance and equivalent. The fact that you land on one heads value or the other is irrelevant to the problem being asked. What am I missing?

smagboy: hmmm I think I see how you are thinking about this. Does this clear it up: if you`re looking at one side of the two-headed coin, there`s a 100% chance the other side is also head. If you`re looking at the 2nd side of the two-headed coin, there`s a 100% chance the other side is also a head. If you`re looking at the head of the standard coin, there`s a 0% chance. so it`s (1+1+0)/3. Not sure if that helps or not. The key point is the double sided coin can.

There`s another problem, if you flip two regular coins, what is the probability you will get two heads, two tails, and one head one tail? it`s not 33% each. there`s only 1 way you can get two heads or two tails, but 2 different ways you can get 1 head and one tail. so it`s actually 25% for both heads, 25% for both tails, and 50% one head one tail. Not sure if that helped.

paperduck, I really do understand what you`re saying. I wish I could get out into words what`s in my head, but, I guess what I`m saying is that, since we`re not differentiating between the heads on one side of the two-headed coin and the other, and since the problem is asking for heads, that coin doesn`t really have a 50/50 chance of landing on one side or the the other, it`s got 100% chance of meeting the conditions. It`s going to land on heads. Period. So, if we were calling it Heads1 and Heads2, and only one of those satisfied the conditions, then, yes, 2 in 3 chances. But, since *either* heads value satisfies the conditions of the equally, and since, once we`ve drawn a heads, the other one has 100% chance of showing is we have the two-headed coin, I see it as a 1 of 2.

But I still may be wrong, and happily admit it. I suppose it`s kind of like the Monty Hall conundrum, eh? Except, in this case, one of the covered doors exactly equals the one we have already.

The word "ALSO" makes it 50%. "What is the probability that the other side also shows heads." with this stipulation, we now have a 50% chance that the other side will show a head.

It isn`t asking what the likelihood of the coin showing heads on the other side is. It only asks what is the probability of pulling the two headed coin out of a bag.

There are 4 possible outcomes when you draw a coin:

Normal Coin Heads Normal Coin Tails Double Coin Heads 1 Double Coin Heads 2

At which point there is 50/50 chance of drawing either coin.

But, when you look at the coin and see Heads, you can eliminate the Normal Tails outcome from the list above. That leaves 3 possible scenarios. Two of those three possible scenarios has a Heads on the opposite side, so the result is 2/3 (67%).

Consider this version, you take the 4 aces from a deck of cards and randomly give them to 4 people. You want to guess who has the Ace of Spades and your choice is only 1 in 4. You ask one of the people which card they have and they have the Heart. Now, your chances of guessing right from the remaining people is 1/3 because you have more information, it does not stay at 1/4 (which is more or less those making the 50/50 argument about the coins are claiming).

Ogen - The use of the word "Also" does not change anything. If it were a blind draw, you are right that the chance of drawing the double headed coin is 50%. But, it isn`t, we draw the coin and gain more information. Since we are looking at a Heads, we can use that information to adjust our guess.

you can also took at it this way too, for this particular problem, they say, what is the probability that "the other side ""also"" shows heads". this wording is saying that the original draw is infact heads. considering the question is asking if the coin you get has heads, then what is the chance the other side will be heads. there are only 2 possible outomes given you dont draw the clover as depicted in the video. reguardless of which coin you pick, once fliped over, it will only have 2 possible outcomes, a head or a clover since thoes are the only faces posible. thus, it can only be a 50-50. their answer is 2/3, but i would think this implies your favoring one coin over the other, or that there is a third double face coin.

- This one is pretty straight forward
You have a 50/50 chance of getting the two headed coin. After you pull it out it doesn`t matter what is showing, it`s still 50/50 it will be heads on the other side.

I think 2/3 is wrong.

There`s a 75% chance that the coin you select will show heads. Therefore, there are 3 remaining possibilities for the other side of the coin that you did select: 1) side B of the regular coin (tails); 2) side A of the two-headed coin (heads); or side B of the two-headed coin (heads). Out of those 3 possibilities, the odds are 2/3 that the other side is heads.

Because you initially drew heads, you eliminated one of the 4 possibilities. There are still 2 chances that there is a head on the other side, but that is now 2 out of only 3 remaining possibilities.

The side showing does matter on the first coin. 3/4 times heads will show while 1/4 of the times tails will show. But if the first coin shows tails then 1/1 times the other side is heads. The 1/1 math works the same as the 2/3.

"What`s the probability that the other side ALSO shows heads."

So your side needs to be showing heads, and the other side needs to show heads.

There are 2 coins, 1 of them has 2 heads, the other doesn`t.

Hence 50% chance. Either you pulled that coin or you didn`t.

Someone used it as a scam in the show to cheat someone.

As Fwoggie2 said, "It`s the specific wording.

"What`s the probability that the other side ALSO shows heads." "

There are 4 outcomes in this case:

Double Coin Heads, Flip Double Coin Heads

Double Coin Heads, Flip Double Coin Heads

Other Coin Heads, Flip other coin shamrock

Shamrock Coin, Flip other coin Heads

Since Shamrock is eliminated right away when you pull it, only the other 3 options count, making it 2/3 chance of being heads.

Original trick with cards: Normal Joker, Double sided back of card. Outcomes as follows:

Double Card Back, Flip Double Card Back

Double Card Back, Flip Double Card Back

Joker backside, Flip Joker

Joker Faceside would call for a redo.

4 outcomes, 50% being backside of a card, 25% Joker, 2

You are drawing sides of a coin, so there are 4 possibilities in the first draw. 1 of them is not considered (drawing tails).

You pull out the coin and see heads. It`s either the 1st side of the double-sided coin, the second side of the double-sided coin, or the heads side of a standard coin. When you flip it over, 2 of the 3 possibilities will reveal heads again.

You have a 50% chance of selecting the normal coin overlapped by a 50% chance in first viewing it from the clover perspective.

It`s 75/100...

Once heads is drawn, there are only two possible outcomes with that given: that you are holding the double-headed coin, thus the other side is heads, *or*, that you`re holding the standard coin and the other side is tails.

Once you`ve drawn heads initially, those are the ONLY two possibilities. So, it`s 50/50 under the given circumstances, IMHO.

If I`ve drawn the shamrock coin, the probability of the other side that the other side also shows heads is 0, because either the face I`m looking at is a shamrock, or the other face is the shamrock. This is why the wording is so important - the other side must ALSO a head. This is impossible with the Shamrock coin, regardless of which face you`re looking at.

I`ve I`ve drawn the double headed coin, obviously the other side is a head, so the probability is 1 (100%).

(0+1)/2 = 50%.

Even if we hadn`t already drawn, the two-headed coin`s two outcomes are exactly equal if you`re looking for heads and only heads (e.g. if that`s your condition), so, as such, landing on heads for that coin is a 100% chance and equivalent. The fact that you land on one heads value or the other is irrelevant to the problem being asked. What am I missing?

There`s another problem, if you flip two regular coins, what is the probability you will get two heads, two tails, and one head one tail? it`s not 33% each. there`s only 1 way you can get two heads or two tails, but 2 different ways you can get 1 head and one tail. so it`s actually 25% for both heads, 25% for both tails, and 50% one head one tail. Not sure if that helped.

But I still may be wrong, and happily admit it. I suppose it`s kind of like the Monty Hall conundrum, eh? Except, in this case, one of the covered doors exactly equals the one we have already.

The word "ALSO" makes it 50%. "What is the probability that the other side also shows heads." with this stipulation, we now have a 50% chance that the other side will show a head.

It isn`t asking what the likelihood of the coin showing heads on the other side is. It only asks what is the probability of pulling the two headed coin out of a bag.

Normal Coin Heads

Normal Coin Tails

Double Coin Heads 1

Double Coin Heads 2

At which point there is 50/50 chance of drawing either coin.

But, when you look at the coin and see Heads, you can eliminate the Normal Tails outcome from the list above. That leaves 3 possible scenarios. Two of those three possible scenarios has a Heads on the opposite side, so the result is 2/3 (67%).

Consider this version, you take the 4 aces from a deck of cards and randomly give them to 4 people. You want to guess who has the Ace of Spades and your choice is only 1 in 4. You ask one of the people which card they have and they have the Heart. Now, your chances of guessing right from the remaining people is 1/3 because you have more information, it does not stay at 1/4 (which is more or less those making the 50/50 argument about the coins are claiming).