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• 2021 AIME II Problems/Problem 8
  ...lected at random so that each of the possible moves is equally likely. The probability that after exactly <math>8</math> moves that ant is at a vertex of the top Finally, the requested probability is <cmath>\frac{N(8,\mathrm{BT})+N(8,\mathrm{TT})}{N(8,\mathrm{BB})+N(8,\ma
  17 KB (2,722 words) - 18:32, 23 January 2023
• 2022 AIME II Problems/Problem 2
  ...c34</math>. Assume that outcomes of different matches are independent. The probability that Carl will win the tournament is <math>\frac{p}{q}</math>, where <math> ...h> players, and the arrow is from the winner to the loser with the winning probability as the label.
  4 KB (673 words) - 16:15, 24 January 2023
• 2021 Fall AMC 12B Problems/Problem 23
  ...utive integers out of <math>{30 \choose 2}</math> possible pairs, thus the probability that any given pair is consecutive is <math>\frac{29}{{30 \choose 2}}</math [[Category:Intermediate Combinatorics Problems]]
  15 KB (2,241 words) - 00:38, 6 January 2023
• 2021 Fall AMC 12B Problems/Problem 17
  ...grid lines randomly and independently with equal probability. What is the probability that after <math>5</math> moves the bug never will have been more than <mat ...) = 6C(4) + 3V(4) = 6 \cdot 60 + 3 \cdot 192 = 936,</math> and the desired probability is thus <math>\frac{936}{6^5} = \boxed{\textbf{(A)}\ \frac{13}{108}}.</math
  8 KB (1,309 words) - 00:31, 6 January 2023
• Class Badges
  Finish all challenge problems for a single lesson. Answer three problems correctly in a row.
  2 KB (430 words) - 13:36, 31 May 2024
• 2023 AIME I Problems/Problem 6
  ...guess the color with <math>a</math> unrevealed cards, which succeeds with probability <math>\frac{a}{a+b}.</math> There are always <math>3</math> unrevealed cards of each color, so the probability of guessing correctly is <math>\frac{1}{2}</math>.
  11 KB (1,654 words) - 17:28, 31 January 2024
• 2023 AIME II Problems/Problem 6
  ...e chosen independently and uniformly at random from inside the region. The probability that the midpoint of <math>\overline{AB}</math> also lies inside this L-sha ...right square. This occurs with <math>\frac{2}{3} \cdot \frac{1}{3}</math> probability.
  7 KB (1,245 words) - 12:48, 1 February 2024
• Know the Facts: Gmaas
  ...roblem. Therefore, I proved that you cannot use the Gmaas theorem to solve problems. But using theorem 3.141592653589793238462643383 "2. Gmaas can turn things ...oblems, which has around 73,000 bytes. EDIT: Gmaas has beaten 2008 most iT Problems! It is the longest AoPS Wiki article ever. Gmaas's article has 89,119 bytes
  88 KB (14,928 words) - 13:54, 29 April 2024
• 2023 AMC 12A Problems/Problem 17
  ...revious jumps, Flora leaps a positive integer distance <math>m</math> with probability <math>\frac{1}{2^m}</math>. What is the probability that Flora will eventually land at 10?
  7 KB (1,072 words) - 10:46, 22 February 2024

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