Consider the 6 × 6 square in the figure. Let A _ 1 , A _ 2 , , A _...

Given,

We have to choose two distinct points randomly,

Now number of ways of selecting $2$ adjacent dots in row will be$= 6$ {as if you pick any dot then you have pick second dot from remaining $6$ dots, so total ways will be $1 \times C1 6 = 6$}

Similarly, number of ways of selecting $2$ adjacent dots in column$= 6$

$∴$Number of ways of selecting $2$ adjacent dots from the given diagram we will $= 6 \times 7 + 6 \times 7 = 84$

So, probability is given by,

$p = \dfrac{84}{C2 49} = \dfrac{84 \times 2}{49 \times 48}$

$⇒ 7p = \dfrac{7 \times 84 \times 2}{49 \times 48} = \dfrac{1}{2} = 0 . 5$