Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Comments on Search & Probability

Parent

Search & Probability

+1
−2

Search Grid

Above is a $2 \times 2$ search grid constructed to search for a lost object.

We begin by not knowing anything and hence if F = finding the object in a particular square, $P(F) = \frac{1}{4}$. Figure A.

We check $1$ square and we don't find the object (that's figure B with one square redded out). We now update $P(F)$ for the remaining $3$ squares: $P(F) = \frac{1}{3}$.

We then search a 3rd square (figure C) and update $P(F)$ accordingly, $P(F) = \frac{1}{2}$

From what I can gather, this is a brute search method and although we can compute the probabilities (vide supra), they don't allow us to refine the search (they do not aid us in any way at all because all the options are equiprobable).

Question: Is there a way we can "remedy" this i.e. (somehow) make $P(F)$ different for each square, which would allow us to shorten the path to finding the lost object (vide infra)

Search Grid 2

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

Well, I guess you could find a piece of paper with additional information in the visited square. *Som... (3 comments)
Post
+5
−0
Is there a way we can "remedy" this

No, not without additional information. If you truly do not know anything about the location of the lost object other than it is not in any of the squares you searched, then there is always an equal chance of it being in each of the unsearched squares.

How about if I randomly (???) sweep sections of the squares left. Divide the 3 remaining squares into equal parts and conduct variable searches in these parts.

You are trying to get something from nothing. You have no information about the location of the object, so the only way to get information is to search. Every place you look has the same chance of having the object in it as any other place of the same size.

If you break up the 3 remaining squares into 3 equal boxes each, then you now have 9 boxes the object could be in. Each box is 3x easier to search, but also with 3x less chance the object is there.

History
Why does this post require attention from curators or moderators?
You might want to add some details to your flag.

1 comment thread

Firstly, gracias for the answer. What kind of *additional information* would be required? Is there... (2 comments)
Firstly, gracias for the answer. What kind of *additional information* would be required? Is there...
Hudjefa‭ wrote 4 months ago

Firstly, gracias for the answer.

What kind of additional information would be required? Is there some way to reduce the number of steps (the lost object is in one of the $4$ squares) to discovery of the lost object?

How about if I randomly (???) sweep sections of the $3$ squares left. Divide the $3$ remaining squares into equal parts and conduct variable searches in these parts. For example I now subdivide each of the remaining $3$ squares into thirds, giving us a total of $9$ smaller rectangles. After that I could vary (advisable?) how many of the rectangles/square I search: I could search $2$ of the rectangles in one square, $1$ each for the other $2$ squares. Does this "technique" reduce the number of steps relative to the brute search method we were using?

celtschk‭ wrote 4 months ago

If you know in advance that the thing you search is in one of those four smaller rectangles (rather than anywhere in the 9 rectangles that make up the three squares), that would be exactly the kind of information which would change the probability. Except that if you knew it before even searching the first square, the probabilities for the four squares would not be $1/4$ each (if you had no further information about the first square, the initial probabilities would be $3/7$, $2/7$, $1/7$, $1/7$). But if you learned it during the search of square one, the update to that would be possible.