Calculating the Probability of Finding a Word in a Word Search Puzzle

[Alfonso]

Howdy,

I'm completely not sure how to go about this problem. I feel like there is more than one way to approach this problem. I just know words can go forwards, backwards, and diagonal and just get stuck there. So here it is:

What is the probability that a letter in a given position within a 25x25 word
search puzzle is the first letter of a randomly chosen three-letter word beginning with the
letter "T"? In your calculations, assume that the letter of choice is "interior" to the puzzle,
in the sense that it is not possible to "leave" the puzzle by going two letters in any of the
allowed directions. Repeat the calculation (with the same proviso about letter position) for
one of seventeen speci cally chosen four-letter words.
Suppose you were offered a wager whereby you paid $1 to a bookie, who would return $2
if one of the seventeen words is in the puzzle, but would keep your dollar otherwise. Would
you take the bet? What is the expectation value of your cash flow in this transaction?

Thanks guys! :)

 

[thebigstar25]

please show your work ..

 

[Alfonso]

I don't really have any work because I don't know how to approach this problem. I mean what I tried to do was draw a picture, a 25x25 grid just to try and illustrate it. And then since it says to leave it by two blocks I shaded two block in every direction so it's more like a 23x23. That's it. Sorry, I don't know what to do :(