Question

There are $4$ horizontal and $6$ vertical equi-spaced lines. If a rectangle is randomly selected, then the probability that it is a square is

• A. $\frac{7}{45}$
• B. $\frac{13}{45}$
• C. $\frac{11}{18}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{13}{45}$


Total number of rectangles $={}^6{C}_2\times {}^4{C}_2$
Number of $1\times 1$ square $=5\times 3$
Number of $2\times 2$ square $=4\times 2$
Number of $3\times 3$ square $=3\times 1$

Required probability $=\frac{5\times 3+4\times 2+3\times 1}{{}^6{C}_2\times {}^4{C}_2}$
$=\frac{26}{90}=\frac{13}{45}$