Best...Puzzle...Ever....

[Tuzenbach]

Regarding the 3 chests:


What if Monty's bluffing and NONE of the chests hold any treasure? So long as the players don't have a way of discovering this, Monty will win every time, yes?

 

[Nasma]

This one isn't so much an adventuring problem, but I find it interesting nonetheless.

Q: "I have two children, one of whom is a boy. What are the odds that the other is a girl?"

A:

Spoiler

Two out of three

Reason? There are four possiblities regarding the sexes of two children, each equally likely. BB, BG, GB, GG. If one child is a boy, then this leaves BB, BG, GB. Therefore the odds are two out of three.

 

[PennStud77]

This one isn't so much an adventuring problem, but I find it interesting nonetheless.

Q: "I have two children, one of whom is a boy. What are the odds that the other is a girl?"

A:

Spoiler

Two out of three

Reason? There are four possiblities regarding the sexes of two children, each equally likely. BB, BG, GB, GG. If one child is a boy, then this leaves BB, BG, GB. Therefore the odds are two out of three.

Spoiler

No. Since you said ONE is a boy, the order doesn't matter, hence BG and GB are the SAME THING.... so there are only two possibilities BB and BG (which is not so coincidentally identical to saying that there is a 50% chance that EACH child is a boy or a girl, and since you're only wondering about the unknown child, it is 50/50)

 

[MerakSpielman]

I've heard the 3 chests puzzle before, except in the form of the familiar game of 3 upside-down cups, one of which has an object hidden underneith. The gamester mixes up the cups and lets you pick one. Before you get to see what is under it, he flips over one of the other 2 cups, showing that it's empty and gives you a chance to switch your choice. This option is given regardless of whether you picked the right one.

The math is subtle enough that cups gamesters who do this method do rather well financially. It's shockingly annoying -and against all common sense -that the revealed cup doesn't increase your odds of winning at all - it just inspires you to keep playing.

 

[Pyske]

Spoiler

No. Since you said ONE is a boy, the order doesn't matter, hence BG and GB are the SAME THING.... so there are only two possibilities BB and BG (which is not so coincidentally identical to saying that there is a 50% chance that EACH child is a boy or a girl, and since you're only wondering about the unknown child, it is 50/50)

Spoiler

Not quite. You're correct that BG and GB yield the same result, and thus can be combined. However, in combining them, we have to combine their probability, as well. So, the resulting probability is 1/2 compared to the 1/4 of BB. That normalizes to 2/3 and 1/3 respectively.

I have always seen these problems used to impress upon people how bad humans are at intuitively judging statistics and probability. For the record, despite knowing the solution to the chests problem, I still got this wrong at first (intuitive) glance.

. . . . . . . -- Eric

 

[gloomymarshes]

*ahem*

here is my riddle...

O T T F F S S

what comes next?

*ahem*



RX

N

(one two three four...)

 

[MerakSpielman]

Sorry Psyke, but you're wrong and I can prove it.

Spoiler

If you have 2 random children, each has a 50-50 chance of being a boy or a girl. The first one being revealed as a boy doesn't increase the odds of the second one being a girl.

If the first child is a boy, you eliminate two possibilities: GB and GG cannot occur, for the sex of the child in the first position can no longer be a girl.

You have two options remaining: BG and BB. The remaining child does, indeed, have a 50-50 chance of being either sex.

 

[MerakSpielman]

N

(one two three four...)

You skipped "E"

 

[PennStud77]

Spoiler

Not quite. You're correct that BG and GB yield the same result, and thus can be combined. However, in combining them, we have to combine their probability, as well. So, the resulting probability is 1/2 compared to the 1/4 of BB. That normalizes to 2/3 and 1/3 respectively.

I have always seen these problems used to impress upon people how bad humans are at intuitively judging statistics and probability. For the record, despite knowing the solution to the chests problem, I still got this wrong at first (intuitive) glance.

. . . . . . . -- Eric

Spoiler

If they're the same thing, then there IS no separate probability for each.

 

[Pielorinho]

I reluctantly think Nasma is right on this. It may help to divide things into shorter sentences and analyze the probabilities after each.

I have two children. Assuming no hermaphrodites, the possibilities are:
Mary Harry
Tom Harry
Tom Jane
Mary Jane

Yes?

One of them is a boy. That eliminates one of the four possibilities; now we know that my kids are:
Mary Harry
Tom Harry
Tom Jane

Yes?

What are the odds that the other is a girl?
Of the three possibilities, two of them include a girl member. The odds are therefore 2/3.

Daniel