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?
A
Step-by-Step Solution
Key idea: This is a classical probability question on a grid, recognisable because we select 2 items from a structured arrangement and need a geometric condition (common side).
Step 1: Identify the grid dimensions.
64 squares on a square canvas means an grid.
Step 2: Total ways to choose 2 squares from 64.
Step 3: Count favorable pairs (sharing a common side).
Two squares share a side if they are horizontally or vertically adjacent.
- Horizontal pairs: Each of the 8 rows has 7 adjacent pairs. Total = .
- Vertical pairs: Each of the 8 columns has 7 adjacent pairs. Total = .
- Total favorable = .
Step 4: Calculate probability.
Common trap: Including diagonal neighbors. "Common side" means sharing an edge, not a corner.
Answer: 1/18