Probability
Classical Probability
Grade None
Question:
<p>If two of the 64 squares on a chessboard are chosen at random, the probability that they have a side in common is</p>
Step-by-Step Solution
Key Concept: Count horizontally adjacent pairs (7 \times 8 = 56) and vertically adjacent pairs (8 \times 7 = 56). Total adjacent = 112.
<p>Total ways to choose 2 squares: $\binom{64}{2} = 2016$.</p><p>Adjacent pairs sharing a side:</p><ul><li>Horizontal: $7 \text{ per row} \times 8 \text{ rows} = 56$</li><li>Vertical: $7 \text{ per column} \times 8 \text{ columns} = 56$</li></ul><p>Total adjacent $= 112$.</p><p>$P = \dfrac{112}{2016} = \dfrac{1}{18}$</p>
Correct Answer: B