Mathematics - Probability Question with Solution | TestHub

Consider the $6\times 6$ square in the figure. Let $A_1,A_2,\dots ,A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_i$ and $A_j$ are friends if they are adjacent along a row or along a column. Assume that each point $A_i$ has an equal chance of being chosen.

(There are two questions based on $\mathrm{PARAGRAPH} "\mathrm{II}"$, the question given below is one of them)

Let$p_i$be the probability that a randomly chosen point has$i$many friends,$i=0,1,2,3,4$. Let$X$be a random variable such that for$i=0,1,2,3,4$, the probability$P(X=i)=p_i$. Then the value of$7 E\left(X\right)$is