JEE Advanced 2021 · Paper 1, Mathematics question 5

Question Stem for Question Nos. 5 and 6

Three numbers are chosen at random, one after another with replacement, from the set $S = \{1, 2, 3, \ldots, 100\}$. Let $p_1$ be the probability that the maximum of chosen numbers is at least 81 and $p_2$ be the probability that the minimum of chosen numbers is at most 40.