Question

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

• A. $\frac{4}{17}$
• B. $\frac{3}{17}$
• C. $\frac{2}{17}$
• D. $\frac{15}{17}$

Answer 1

The correct option is B $\frac{3}{17}$

Number of square of size:$1\times 1=\left(8\right)\left(8\right)=64$
Number of square of size:$2\times 2=\left(7\right)\left(7\right)=49$
Number of square of size:$3\times 3=\left(6\right)\left(6\right)=36$
Number of square of size:$4\times 4=\left(5\right)\left(5\right)=25$
Number of square of size:$5\times 5=\left(4\right)\left(4\right)=16$
Number of square of size:$6\times 6=\left(3\right)\left(3\right)=9$
Number of square of size:$7\times 7=\left(2\right)\left(2\right)=4$
Number of square of size:$8\times 8=\left(1\right)\left(1\right)=1$
Total number of squares $=64+49+36+25+16+9+4+1=204$
Probability of getting $3\times 3$ square $=\frac{36}{204}=\frac{3}{17}$