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Search & Probability

![Search Grid](https://math.codidact.com/uploads/yyx1za7xq42yh99y7kbhvcq9wgen)

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](https://math.codidact.com/uploads/ii0so3ngh4bk9xlqqb3y6ix0d5a6)