# The ever elusive coin problem

This topic is 4849 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

##### Share on other sites
I think you're correct. The coin you picked is either the H/H or H/T, and it's only one of those two possibilities.

##### Share on other sites
How can there be three possibilities left been H/H/T ? You never can pick up what's on the front of the coins.. only what's on the back.. so the only two possibilities ever are H or T.
So it definitly is 1/2.

##### Share on other sites
Sounds like someone heard about the monty hall problem and tried to apply it to coins. But it's definately 1/2

##### Share on other sites
I agree with your solution of 1/2. The problem (at least as you've put it) actually only deals with the unknown sides of the coins, the top should be completely irrelevant.

##### Share on other sites
The probability that it will be a heads is 1/2. It's obvious and verifiable. The back of the coin is completely tangent to the problem.

##### Share on other sites
After some more thought, I know where the confusion came from. The author checked the possible outcomes from picking up one of these two coins.

Tails

And from that he concluded, that of the three possible outcomes, two of them yeilded heads, therefore the probability of it being heads is 2/3. However, he failed to realise that the fact that the side facing up is guaranteed to be heads consolidated some of his outcomes. Consider the case were we have a H/H coin and a H/T coin, and we don't know what sides are facing up. The probability of the side underneath one of the coints being a heads is 3/4, and the probability of it being a tails is 1/4. As soon as he places a restriction that both sides facing up must be heads, he eliminates the heads side of the tails coin from play. He did that. There is also the added restriction that it is now impossible to obtain a result where two heads are facing down. That means based on the result of one coin, we know what the result of the other coin will be. It consolidates the two heads results, like so:

-Side 1 (1/4)
-Side 2 (1/4)
Tails (1/2)

##### Share on other sites
The description of the problem is ambiguous.

* Are you presented with one of the coins, showing heads, and asked what the probability of the back being tails is?
* Or are your presented with both coins, both showing heads, pick one, and asked what the probability if it being tails is?

The author's result is for the first case. Yours is for the second.

##### Share on other sites
Considering it's a probability it's asking for more than one time; the either heads or tails(50%) might work if this was just once but if done more than once this is what should be correct:

Let's first lable the coin sides.

h1/t1
h2/h3

and list all possible combinations with heads on top.

h1/t1
h2/h3
h3/h2

When you flip the coin over you have a 1/3 chance to get tails.

Remember the coin picked up can be one of the three, you must consider all three heads when concluding what the chance is.

But I think this pretty much sums up the arguments
"The description of the problem is ambiguous.

* Are you presented with one of the coins, showing heads, and asked what the probability of the back being tails is?
* Or are your presented with both coins, both showing heads, pick one, and asked what the probability if it being tails is?

The author's result is for the first case. Yours is for the second."

##### Share on other sites
Quote:
 The description of the problem is ambiguous.* Are you presented with one of the coins, showing heads, and asked what the probability of the back being tails is?* Or are your presented with both coins, both showing heads, pick one, and asked what the probability if it being tails is?The author's result is for the first case. Yours is for the second.

The description isn't ambiguous, it indicates the second case. It would be best to post the original problem as it was stated in the book however, to be sure it isn't a misinterpretation of the question.

1. 1
Rutin
36
2. 2
3. 3
4. 4
5. 5

• 12
• 14
• 9
• 9
• 14
• ### Forum Statistics

• Total Topics
633344
• Total Posts
3011435
• ### Who's Online (See full list)

There are no registered users currently online

×