JEE Advanced 2023 Paper 2 · Q16 · Probability Distributions

PARAGRAPH II — Consider the $6 \times 6$ square in the figure. Let $A_1, A_2, \ldots, A_{49}$ be the points at 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 ___.