Brain teaser thread

[Dauphin]

Originally posted by JohnM2433
Assuming that the host is telling the truth, and that the same thing would have happened no matter which door you picked, which of the remaining doors is more likely to have the grand prize behind it: the one you selected or the other door that the host didn't point out?

Even if there were a thousand other doors and you were shown one was empty, the other doors have a greater chance of holding the grand prize than the one you picked.

[CyberGnu]

Forgot that I'm supposed to put a new riddle in..

What loses its head in the morning,but gains its head at night?

[Urban Ranger]

*bump*

[JohnM2433]

CyberGnu gave the correct answer to my problem. Sagacious Dolphin's observation that the same principle holds for any number of doors (more than two) is also correct; the odds of the original door containing the prize will not change, and indeed cannot, since you must get the same basic information about that door (i.e., none) each time. Or to put it another way, the probability of the door you picked being the correct one when you pick it is the average of the probabilities of it being correct for each other door the host might point out, since he is equally likely to select each one. But since the cases are all symetrical, the probability for the chosen door must be the same in each case, and thus the same as it was originally. Only the odds for the doors you did not select change.

There was another thread in which someone presented the following senario: Of three prisoners, one will die and the other two will go free, but none of them knows which is which. One prisoner asks a guard to give a letter to one of the other prisoners who will go free. The guard does so, and tells him which one. How is it that the prisoner's odds of dying have now increased from 1/3 to 1/2, since they would have been the same if the other of the other two prisoners had gotten the letter?

Well, his odds of dying actually stay the same, and the odds of the other prisoner who didn't get the letter dying go up to 2/3. I posted as much. The comparison to the game show problem is obvious. But now I can't seem to locate that thread. I can't remember its name or what forum it was in, so I would appreciate if anyone could tell me which it was, as I wanted to check in on it.

I'm still trying to get the answer to CyberGnu's latest riddle...

[Zero-Tau]

Time to bump this thread up again.

Now, about the doors riddle...

I agree, the other door has a bigger chance to have the prize. The important fact is that it is always one of the other doors that are opened. If the host randomly chose one of the doors without the prize, so he might open the one you chose, then your chances would be 50-50 afterwards.

The same thing applies to the prisoners. Had the prisoner asked the guard to pick one of the prisoners who was to go free at random, then his odds had increased when the letter was delivered to one of the other two.

And CyberGnu:

[Urban Ranger]

It is a word IIRC. Can't remember what it is.

[CyberGnu]

hehehehehehe

a pillow

someone else ask something

[Urban Ranger]

*grumble*

A pillow does not have a head

[Dry]

A father is 25 years older than his his.
In 7 years, he will have 5 times his son's age.
What is the father doing?

[Ramo]

He's screwing the kid's mom.

[Immortal Wombat]

breathing

[Immortal Wombat]

...heavily

[Ramo]

The kid is -9 months old.

[Urban Ranger]

That doesn't work. The kid needs to be at least 7 years old in 7 years time, so the father needs to be at least 35, not 32.

[Urban Ranger]

Okay, somebody post a question.