Re: Deal or no Deal
- From: "zcx" <zcx@xxxxxxxxxxxx>
- Date: Sun, 26 Feb 2006 05:59:11 GMT
"John Dean" <john-dean@xxxxxxxxxxxxxxxx> wrote in message
news:dtppt4$53t$1@xxxxxxxxxxxxxxxxxxxxxxx
zcx wrote:
"John Dean" <john-dean@xxxxxxxxxxxxxxxx> wrote in message
news:dto92d$727$1@xxxxxxxxxxxxxxxxxxxxxx
Yeah. Weird, innit? You have to distinguish between the probability
(which is set by the way the boxes are originally allocated) and the
reality (about which you may get more information as the boxes are
opened). Try it with a set of playing cards - 11 red and 11 black. Pick
one at
random (face down). The probability it is black is 0.5
Yes, at that point it is.
Draw cards from the remaining 21 one at a time and examine them.
What, in this process, could change the probability that you have a
black card?
Probability is not the same value for all time.
The more blacks you remove, the less likely that the card you have is
black. If you remove all 11 black cards, then the probability that
your card is black = 0.
The reason for this is that the events are *not* independent and
therefore information about one event gives you more information
about what is likely to happen in the others.
How do you think card counting works?
Think about it like this.
I remove 11 blacks from the pack and am left with 2 cards, which I
now know are both red.
What if I leave those 2 cards sitting about for a few days, then give
them to someone else. I tell them they are both red and they claim
the prob. of the facedown card being red is 1.
I say "No, they came from a pack with equal reds and blacks and
therefore the probability of the facedown card being black is 0.5".
They'd suggest medication...
No, because you're into a new event which begins with 2 red cards.
So how long do you have to leave the cards sitting there before a "new
event" begins? An hour, a day, 2 days? Does the probability of getting a
blue from those 2 red cards change from 0.5 to 0 suddenly? Or gradually? Or
with a full moon? Do you have to move them to another place or show them to
another person? Or just say "I declare a new event!"?
Deal or No deal begins with 22 boxes. That sets the probability. You're
mixing what you know about the probabilities with what information you
have discovered.
No, you are mistakenly applying the rules of sampling *with* replacement to
problems of sampling *without* replacement.
Sampling *with* replacement is a toss of a coin, roll of a dice. On your
first roll there is a probability of 1/6 of getting a 6. On your second roll
the probability of getting a 6 is also 1/6 whether you just rolled a 6 or
not. Each roll is independent of any previous ones so the probability is
always the same.
DOND and your 22 card example are sampling *without* replacement. The
probability at the start of you having a red box is 1/2. AFTER the first
pick however the probability of your own box being red is NOT 1/2. It is
either 10/21 or 11/21 depending on whether your first box was red. The
events are not independent, therefore they continually affect and change the
probabilities.
Eventually you get to two boxes left, both are blue(say), so there is NO
chance of you having a red box i.e. by definition, the probability of
picking a blue box when both are red = 0.
The fact that you have picked and left aside a box at the start is totally
irrelevant because it was a random choice. It doesn't assign any special
properties to that box, or to the card which you placed face down. It's just
the same as any other.
.
- References:
- Deal or no Deal
- From: zcx
- Re: Deal or no Deal
- From: LindaMcK
- Re: Deal or no Deal
- From: John Dean
- Re: Deal or no Deal
- From: zcx
- Re: Deal or no Deal
- From: John Dean
- Re: Deal or no Deal
- From: zcx
- Re: Deal or no Deal
- From: John Dean
- Deal or no Deal
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