Probability
Geometric Probability (Grid)
nta_pyq_2025_apr
Grade 12
Question:
A board has 16 squares as shown in the figure (4$\times$4 grid). Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is:
Step-by-Step Solution
Key Concept: Total ways to choose 2 squares: ${}^{16}C_2 = 120$. Count adjacent pairs (sharing a side): 3 horizontal pairs per row $\times$ 4 rows + 3 vertical pairs per column $\times$ 4 columns = 24.
Total $= {}^{16}C_2 = 120$. Adjacent pairs: $3\times4$ (horizontal) + $4\times3$ (vertical) $= 24$. Non-adjacent pairs $= 96$. $P = 96/120 = 4/5$.
Correct Answer: 4/5