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

Plotting the diagram of the given data we get,

Now from above diagram we get,

Number of points having $0$ friend $= 0$
Number of points having $1$ friend $= 0$
Number of points having $2$ friends $= 4$
Number of points having $3$ friends $= 5 \times 4 = 20$

Number of points having $4$ friends $= 49 - 24 = 25$

So, probability distribution table will be,

Now from above table expected value will be given by,

$7 \cdot E\left(X\right) = 7\left(0 + 0 + \dfrac{4}{49} \times 2 + \dfrac{20}{49} \times 3 + \dfrac{25}{49} \times 4\right)$

$⇒ 7 \cdot E\left(X\right) = 7\left(\dfrac{100 + 60 + 8}{49}\right)$

$⇒ 7 \cdot E\left(X\right) = 24$