Question

The probability that a square selected at random from a $8\times 8$ chess board each of size $3\times 3$ is:

• A. $\frac{4}{17}$
• B. $\frac{3}{17}$
• C. $\frac{5}{17}$
• D. None of the above

Answer 1

Answer: (B)

$\frac{3}{17}$

Number of squares of size $1\times 1=\left(8\right)\left(8\right)=64$

Number of squares of size $2\times 2=\left(7\right)\left(7\right)=49$

Number of squares of size $3\times 3=\left(6\right)\left(6\right)=36$

Number of squares of size $4\times 4=\left(5\right)\left(5\right)=25$

Number of squares of size $5\times 5=\left(4\right)\left(4\right)=16$

Number of squares of size $6\times 62=\left(3\right)\left(3\right)=9$

Number of squares of size $7\times 7=\left(2\right)\left(2\right)=4$

Number of squares of size $8\times 8=1$

Total squares $=64+48+36+25+16+9+4+1=204$

Probability of geeting $3\times 3$ square $=\frac{36}{204}=\frac{3}{17}$.

So, option B is correct.