Final answer:
The probability that two randomly chosen squares on an 88 by 88 chessboard share exactly one corner is 1/18, which is answer (A). This is determined by dividing the number of successful outcomes (7744 * 3) by the total number of outcomes (C(7744,2)).
Step-by-step explanation:
The student is asking for the probability that two squares picked at random from an 88 by 88 standard chessboard share exactly one corner.
To solve this, we can look at the total number of ways to select two squares (which is the number of squares on the chessboard choose 2, or C(7744,2)) and the number of ways to pick two squares that share a corner.
There are 7744 squares on the chessboard. Each square has 4 corners. However, the corner of each square is shared by 3 other squares, so we divide the total corners by 4 to get unique sharing corners.
Then, since we are looking for two squares sharing one corner, we can pick any square (7744 ways) and then there are only 3 other squares that share a corner with this one.
Therefore, there are 7744 * 3 ways to pick two squares sharing a corner.
The probability is the number of successful outcomes divided by the total number of possible outcomes, which equals (7744 * 3) / C(7744,2).
After simplifying, we find the probability to be 1/18, so the correct answer is (A) 1/18.