Good thread, guys.
Good thread, guys.
As the original poster can I clarify what I meant in the original question?
By a SINGLE person, I mean "me". If I put in my prize into the envelope and let me and 2 others pick prizes out of the envelope, what are the odds that I get my original prize back? I don't care if the other 2 people get their prize as well, just that I get mine BACK SOMEHOW. Are my odds always 1/3, regardless of where I pick?
The original response to the post seems to make the most sense to me.
THANKS!
Malmo:
You are absolutely correct.
The question is unambiguous:
"what are the odds that a single person gets the prize they originally put into the envelope?"
No point in arguing with the folks if they did not get it the first time
brain fart wrote:
As the original poster can I clarify what I meant in the original question?
By a SINGLE person, I mean "me". If I put in my prize into the envelope and let me and 2 others pick prizes out of the envelope, what are the odds that I get my original prize back? I don't care if the other 2 people get their prize as well, just that I get mine BACK SOMEHOW. Are my odds always 1/3, regardless of where I pick?
If that how you define, then yes, your chance is 33.3%, just as long as the other two have to make random choices too..
malmo wrote:
If that how you define, then yes, your chance is 33.3%, just as long as the other two have to make random choices too..
And we all lived happily ever after.
Amen.
Now, what if when the first player chooses, the host opens one of the other envelopes and reveals that it contains a goat? Should the player switch?
Yes, Monty Hall, if one of the remaining envelopes is shown to have someone elses prize (a goat) and you have an opportunity to switch, do it.
Depends if the host knows what is in the envolopes.
I would have answered the first question as 1/3.
You have 2 cases that you will get your prize and four chances you won't.
What is the expected value of the number of people who will pick the prize they originally put into the envelope.
What would it be if there were more people, let's say 10?
Even simpler wrote:
What is the expected value of the number of people who will pick the prize they originally put into the envelope.
What would it be if there were more people, let's say 10?
1/3 * 3 = 1
and
1/10 * 10 = 1
or, more generally
1/n * n = 1
you're kidding, right?
The New UncleB wrote:
Malmo:
You are absolutely correct.
The question is unambiguous:
"what are the odds that a single person gets the prize they originally put into the envelope?"
No point in arguing with the folks if they did not get it the first time
It's funny that you would post this, considering that right after you did, the original poster came in and clarified that he meant exactly what Malmo (and you, by association) claimed he DIDN'T.
The fact that you guys were so confident that he meant one thing, while he meant another, means that it was, by definition, ambiguous.
I don't know if this is the real uncle b or not, but either way, if the (idiot) shoe fits...
The question was crappily phrased, and you guys should have had no problem seeing that.
An Engineer wrote:
It's funny that you would post this, considering that right after you did, the original poster came in and clarified that he meant exactly what Malmo (and you, by association) claimed he DIDN'T.
The fact that you guys were so confident that he meant one thing, while he meant another, means that it was, by definition, ambiguous.
I don't know if this is the real uncle b or not, but either way, if the (idiot) shoe fits...
The question was crappily phrased, and you guys should have had no problem seeing that.
Engineer guy. I never made any claims to what the OP meant to say. I only answered the question to what he actually did say.
"The question is: what are the odds that a single person gets the prize they originally put into the envelope?"
"A single person" is not a matter of formal logic, hillbilly logic, or a walk on a semantics gymnastics beam. A single person means "one person." It does not mean "two persons", or "three." Nor does it mean "zero persons."
I'm not sure what you mean that "you guys should have no problem seeing that it was crappily phrased?" I answered the question that was asked.
What exactly is the purpose of your post? I missed your contributions to the thread.
malmo wrote:
"A single person" is not a matter of formal logic, hillbilly logic, or a walk on a semantics gymnastics beam. A single person means "one person." It does not mean "two persons", or "three." Nor does it mean "zero persons."
malmo,
Just curious, but would you say the same about "someone"? It, by definition courtesy of Cambridge Dictionary, means, "used to refer to a single person when you do not know who they are or when it is not important who they are." There you go, "someone" means a single person. But if we said, "What are the odds that someone picks his own envelope?" would that change how you think the question should be interpreted?
If you were home one evening, and a friend called and asked, "I just wanted to check, will someone be there at noon tomorrow so I can drop off your jacket?" but you knew both you AND your wife would be there, would you answer "No"?
I'm not sure why you can't just admit that the question was ambiguously phrased, especially considering that you yourself interpreted it differently than the OP intended.
"Would you like Coke or Sprite?"
"Yes, please."
malmo wrote:
"A single person" is not a matter of formal logic, hillbilly logic, or a walk on a semantics gymnastics beam. A single person means "one person." It does not mean "two persons", or "three." Nor does it mean "zero persons."
If I went to the grocery store to pick up some beer, and I came home empty-handed and said "I went to the grocery store and there was not a single person there!", what would you think I meant?
By your definition, the grocery store could have been very busy, and thus I was unwilling to wait, and my usage of "single person" would be correct. However, this is NOT common usage. If someone says "there was not a single person," they don't generally mean "there were either zero or more than two people." If you and your buddies are going drinking, and one of you goes into the bar to see how busy it is, and finds it packed, it would be pretty damn silly to say "there isn't a single person in there!" even if it is "technically" correct. There is a difference between the literal translation of a phrase and its common meaning.
The point is that, while your answer was completely correct for one case, it was unclear what ACTUAL case the poster was asking about. I have no problem with your answer, but I do think your (and others) insistence that it was the ONLY way the question could be interpreted is ridiculous.
the other version of the question is posed in the thread title: "What are my odds of picking the right prize?"
"Depends if the host knows what is in the envolopes."
This!