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It also implies that it can't be HT or TH, depending on which coin was looked at. |

And if we do not have that information? If we do not know which coin was looked at, which is the intention (i.e. that's unknown).

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P(HH' | HT) is "what's the probability of NOT heads-heads, given that it actually is heads-tails". |

I toss two fair coins. I look at them and then I tell you truthfully that the coins are definitely NOT both heads, or NOT both tails, depending on what I saw.So, given this, what is the probability that they are both the same? |

EDIT: crap actually I was misreading the problem. Hahahaha

It's still totally 50% though.

It's still totally 50% though.

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P(HH') = 1 - P(TT'). Again I disagree. I think P(HH') is 3/4. I think P(TT') is 3/4. |

This is not your original question. |

Could well be. As I did say at the start, the answer was 1/3 and I have changed the wording, searching for a less ambiguous wording. Sounds like I didn't find it.

As stated previously, it's an ( obviously bad) attempt to turn this original question:

The question above is an attempt to make the following question more intuitive: "I've got two children and I promise you they're not both girls; what are the chances that they're both boys?" The answer is 1/3, but people seem to either insist on 1/2, or insist on altering the question until the answer is 1/2. |

That said:

P(HH' | HT) is "what's the probability of NOT heads-heads, given that it actually is heads-tails". |

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Once again, HH' is not the same set as ¬HH. |

I think HH' means "anything other than heads-heads". Is that true? If so, I think P(HH') is 3/4. If it's not true, what does HH' mean?

Actually no my program still works for this problem! Hooray.

Given what you said here Moschops:

I challenge you to find the logical fallacy in my post here:

http://cplusplus.com/forum/lounge/88256/#msg473370

Or in my program proving this results in 50% here:

http://cplusplus.com/forum/lounge/88256/#msg473380

Given what you said here Moschops:

Moschops wrote: |
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I'll look at one of them at random and tell you the coins are definitely not both <other side of the coin I looked at> (because that way, I also do not have any information that you don't - I don't know what they are any more than you do). |

I challenge you to find the logical fallacy in my post here:

http://cplusplus.com/forum/lounge/88256/#msg473370

Or in my program proving this results in 50% here:

http://cplusplus.com/forum/lounge/88256/#msg473380

As I did say at the start, the answer was 1/3 and I have changed the wording, searching for a less ambiguous wording. |

The answer to this problem:

What's the probability of HH given that ¬TT? |

P(HH | ¬TT) = P(¬TT | HH)P(HH) / (P(¬TT | HH)P(HH) + P(¬TT | HT)P(HT) + P(¬TT | TH)P(TH) + P(¬TT | TT)P(TT)) =

= P(¬TT | HH) / (P(¬TT | HH) + P(¬TT | HT) + P(¬TT | TH) + P(¬TT | TT)) =

= 1 / (1 + 1 + 1 + 0) =

= 1/3

Which is obvious. If it's not one of the four things, it has to be one of the other three, which still have uniform distribution.

I think HH' means "anything other than heads-heads". Is that true? If so, I think P(HH') is 3/4. If it's not true, what does HH' mean? |

Let HH, TH, HT, and TT be the coin configurations, and TT' be you saying "it's not double tails". |

Disch, nothing doing I'm afraid. It was badly worded (which is what I'm working on) so I'm chucking the whole lot out now :) Hopefully the new wording works better (along the lines of "I've tossed two coins and I'm telling you it's not tails-tails, and I'm not telling you anything else at all. What are the odds it's heads-heads?" which then becomes "I've got two children and I'm telling you they're not girl-girl. What are the odds they're boy-boy?")

Aha. P(TT') isn't the probability that it's not tails-tails. it's the probability that I SAY it's not tail-tails. Missed that.

Like I said, this was the first thing I defined: Let HH, TH, HT, and TT be the coin configurations, and TT' be you saying "it's not double tails". |

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Tell you what Moschops:

If I ever meet in you real life, we'll have to get together and do some gambling. You can flip the coins, tell me they're not HH or not TT, and I'll bet with 2:1 odds that the flips came out the same. I'll take that bet any day of the week.

If I ever meet in you real life, we'll have to get together and do some gambling. You can flip the coins, tell me they're not HH or not TT, and I'll bet with 2:1 odds that the flips came out the same. I'll take that bet any day of the week.

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I'm sorry guys, I still respect you, but wtf?

@Moschops

Effectively, regardless of which coin you look at, only one of the two possibilities of the coins being different is possible. It's also only possible for them to be the same. A coin doesn't magically get three sides so the odds are 1:2

To put this simply. You have two possible same scenarios. HH or TT. We can rule one of them out, but you're also effectively ruling out one of the HT or TH possibilities too, without knowing you are.

No matter how you word any problem that involves two sets of two, there is only a 50% chance of the final outcome when one is revealed. Eliminating one of the two, leaves one item left with two possibilities, which is exactly where the 50% chance comes from. You can spin it, twist it, slice it up and dice it, but something that has only two possible outcomes can't magically grow a third.

@Disch

I have some gambling games if you're interested, but be warned, the odds aren't forever in your favor.

@Moschops

Effectively, regardless of which coin you look at, only one of the two possibilities of the coins being different is possible. It's also only possible for them to be the same. A coin doesn't magically get three sides so the odds are 1:2

To put this simply. You have two possible same scenarios. HH or TT. We can rule one of them out, but you're also effectively ruling out one of the HT or TH possibilities too, without knowing you are.

No matter how you word any problem that involves two sets of two, there is only a 50% chance of the final outcome when one is revealed. Eliminating one of the two, leaves one item left with two possibilities, which is exactly where the 50% chance comes from. You can spin it, twist it, slice it up and dice it, but something that has only two possible outcomes can't magically grow a third.

@Disch

I have some gambling games if you're interested, but be warned, the odds aren't forever in your favor.

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