JEE Advanced 2023 Paper 2 Mathematics Q16

Mathematics

Problem

Consider the 6 × 6 square in the figure. Let A₁, A₂, …, A₄₉ be the points of intersections (dots in the picture) in some order. We say that Aᵢ and Aⱼ are friends if they are adjacent along a row or along a column. Assume that each point Aᵢ has an equal chance of being chosen. Let pᵢ 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) = pᵢ. Then the value of 7E(X) is ___.

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