JEE Mains · Maths · STD 11 - 14. probability
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :
- A \(\frac{2}{7}\)
- B \(\frac{1}{18}\)
- C \(\frac{1}{7}\)
- D \(\frac{1}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{18}\)
Step-by-step Solution
Detailed explanation
Total ways of choosing square \(={ }^{64} \mathrm{C}_{2}\) \(=\frac{64 \times 63}{2 \times 1}=32 \times 63\) ways of choosing two squares having common side \(=2(7 \times 8)=112\) Required probability \(=\frac{112}{32 \times 63}=\frac{16}{32 \times 9}=\frac{1}{18}\).
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