This one is pretty straight forward

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This one is pretty straight forward

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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).

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.

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.

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.

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?

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%.

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.

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...

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.

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

"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.

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.

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.

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.

- This one is pretty straight forward