Question

Consider a regular 8x8 chessboard, which consists of 64 squares in 8 rows and 8 columns. There are 1296 different rectangles that can be drawn on the chessboard, comprised entirely of chessboard squares. One of the rectangles is chosen at random. What is the probability that it is square shaped? Present your answer in an irreducible fraction.

Answer 1

Answer)

Probability is given by favorable/total

Here, total number of rectangles = 1296

So, total is 1296

And favorable is the number of rectangles that are square shaped = 64

Therefore, required probability is = 64/1296

= 4/81