JEE Advanced 2023 Paper 2 · Q17 · Probability
PARAGRAPH II (continued) — Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7p$ is ___.
Reveal answer + step-by-step solution
Correct answer:0.5
Solution
Number of unordered friendship pairs (edges of the grid graph): horizontal pairs = $7\cdot 6 = 42$; vertical pairs = $6\cdot 7 = 42$; total $= 84$. Total pairs $= \binom{49}{2} = 49\cdot 48/2 = 1176$. So $p = 84/1176 = 1/14$. Therefore $7p = 7/14 = 0.5$.
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