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

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Consider the 6 &#215; 6  square in the figure. Let A 1 , A 2 , &#8230; , 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 PARAGRAPH &#160; &#34; II &#34; , 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 &#160; E ( X ) is

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Correct answer: A. 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 &#215; 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 &#183; E X = 7 0 + 0 + 4 49 &#215; 2 + 20 49 &#215; 3 + 25 49 &#215; 4 &#8658; 7 &#183; E X = 7 100 + 60 + 8 49 &#8658; 7 &#183; E X = 24

JEE Advanced Mathematics Question (2023) — Solution

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