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Consider the \( 6\times6 \) square in the figure. Let \( A_1, A_2, \ldots, A_{49} \) 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.
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 \( 7E(X) \) is:
