Probability Crossword Puzzle?

• Feb 3rd 2010, 11:17 PM
Alfonso
Probability Crossword Puzzle?
Howdy,

First of all, I hope this problem falls under "probability". I think it does but I'm not quite sure. I thought of maybe posting it under the "puzzles" but here it is.

I'm completely not sure how to go about this problem. I feel like there is more than one way to approach this. 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 everyone for pitching in! :)