Question

A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?

Accepted Answer

A. Grid is $8 	imes 8$. Total pairs of squares = $\binom{64}{2} = \frac{64 	imes 63}{2} = 2016$. Horizontal adjacent pairs per row = 7, total across 8 rows = $7 	imes 8 = 56$. Vertical adjacent pairs per column = 7, total across 8 columns = $7 	imes 8 = 56$. Total favorable pairs = $56 + 56 = 112$. Probability = $\frac{112}{2016}$.

Grid Board Adjacent Squares Probability

Explanation

Practise this under exam conditions