Create the page "Intermediate Probability Problems" on this wiki! See also the search results found.

• 2007 iTest Problems/Problem 44
  ...> and <math>b</math> are natural numbers such that <math>a/b</math> is the probability that <math>N</math> and <math>n^3-36n</math> are relatively prime, find the ...nce a number is picked at random from <math>2007^{2007}</math> values, the probability that <math>N</math> and <math>n^3 - 36n</math> are relatively prime is <mat
  2 KB (305 words) - 23:24, 14 June 2018
• 2007 iTest Problems/Problem 59
  ...y many games (eh, they're in Physicist Heaven, we can bend the rules), the probability that they are ever tied in total wins after they start (they have the same ...number of Fermi wins followed by the number of Feynman wins, and call the probability of Fermi winning <math>p</math>.
  3 KB (528 words) - 10:56, 16 April 2024
• Mock AIME 5 2005-2006 Problems/Problem 7
  ...also lands completely within one of the circles. Let <math>P</math> be the probability that, when flipped onto the grid, the coin lands completely within one of t [[Category:Intermediate Number Theory Problems]]
  853 bytes (134 words) - 21:18, 8 October 2014
• 2012 UNCO Math Contest II Problems/Problem 8
  The probability that a six is rolled on any given roll is <math>1/6</math>, so on average i [[Category:Intermediate Combinatorics Problems]]
  919 bytes (151 words) - 15:09, 1 August 2020
• 2014 UNCO Math Contest II Problems/Problem 8
  ...Alice makes the first hit and alternates hits with the Queen, what is the probability that Alice Now what is the probability that Alice is the first player to hit the goal post with the ball?
  1 KB (185 words) - 03:32, 13 January 2019
• 2014 UNCO Math Contest II Problems/Problem 9
  In the Queen’s croquet, as described in Problem <math>8</math>, what is the probability that the ball hits the Zero probability for <math>n=1</math> and <math>\frac{F_{n-1}}{2^{2n}}</math> for <math>n\ge
  493 bytes (80 words) - 03:32, 13 January 2019
• 2014 UNCO Math Contest II Problems/Problem 10
  ...uests make their guesses at random, perhaps by tossing a coin. What is the probability (b) Tweedledum is the first guest to arrive. What is the probability that one or the other of Tweedledee
  2 KB (297 words) - 03:33, 13 January 2019
• 1988 AHSME Problems/Problem 28
  An unfair coin has probability <math>p</math> of coming up heads on a single toss. Let <math>w</math> be the probability that, in <math>5</math> independent toss of this coin,
  2 KB (240 words) - 14:50, 27 February 2018
• 1987 AHSME Problems/Problem 26
  <math>2</math> and <math>1</math> in the second. What is the probability that the two integers sum to <math>3</math>? [[Category: Intermediate Algebra Problems]]
  2 KB (235 words) - 13:01, 31 March 2018
• 1986 AHSME Problems/Problem 22
  ...rs are picked at random from <math>\{1,2,3,\ldots,10\}</math>. What is the probability that, among those selected, the second smallest is <math>3</math>? [[Category: Intermediate Combinatorics Problems]]
  1 KB (159 words) - 18:37, 12 May 2021
• 2015 UNCO Math Contest II Problems/Problem 8
  at a time, without any going back in. What is the probability that the sequence of numbers [[Category:Intermediate Probability Problems]]
  887 bytes (138 words) - 03:35, 13 January 2019
• 2015 AMC 10A Problems/Problem 25
  ...ts are chosen independently at random on the sides of <math>S</math>. The probability that the straight-line distance between the points is at least <math>\dfrac ...lity. (Alternatively, one can set up a coordinate system and use geometric probability.)
  8 KB (1,406 words) - 19:14, 9 October 2023
• 2018 UNCO Math Contest II Problems/Problem 7
  positive integers less than or equal to twelve. What is the probability that <math>x</math> is a multiple of By counting the number of solutions, the required probability <math>=\frac{1\times1 + 5\times11}{12\times12} = \frac{56}{144} = \frac{7}{
  2 KB (261 words) - 11:57, 26 September 2022
• Gmaas
  ...roblem. Therefore, I proved that you cannot use the Games theorem to solve problems. But using theorem 3.141592653589793238462643383 "2. Games 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
  69 KB (11,805 words) - 20:49, 18 December 2019
• 2016 UNCO Math Contest II Problems/Problem 5
  probability 10%), be rolled back down into the valley (with probability 50% ), or be split by a thunderbolt into two rocks that are both rolled down into the valley (with probability 40%).
  964 bytes (160 words) - 04:02, 13 January 2019
• 2016 UNCO Math Contest II Problems/Problem 6
  (a) Given the situation in Question <math>5</math>, what is the probability that first morning, what is the probability that the Olympian rocks are never all vaporized?
  974 bytes (151 words) - 04:03, 13 January 2019
• 2017 AMC 12A Problems/Problem 22
  ...e 12 lattice points in the interior of one of the sides of the square. The probability that it will hit at a corner rather than at an interior point of a side is We let <math>c, e,</math> and <math>m</math> be the probability of reaching a corner before an edge when starting at an "inside corner" (e.
  4 KB (588 words) - 16:19, 17 May 2024
• 2017 AMC 12B Problems/Problem 22
  ...ts the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins? ...th> ways for this to happen, along with <math>12^3</math> total cases. The probability we're asking for is thus <math>\frac{45}{(12^3)}= \boxed{\textbf{(B)}\frac{
  12 KB (1,935 words) - 11:37, 16 December 2023
• 2017 AMC 12B Problems/Problem 20
  ...and uniformly at random from the interval <math>(0,1)</math>. What is the probability that <math>\lfloor\log_2x\rfloor=\lfloor\log_2y\rfloor</math>? ...g the formula for the sum of an infinite geometric series, we get that the probability is <math>\frac{\frac{1}{4}}{1 - \frac{1}{4}} = \boxed{\textbf{(D)}\frac{1}{
  2 KB (327 words) - 17:24, 27 September 2022
• 2018 AIME II Problems/Problem 6
  ...hosen randomly and uniformly from the interval <math>[-20, 18]</math>. The probability that the roots of the polynomial [[Category:Intermediate Algebra Problems]]
  2 KB (286 words) - 12:20, 27 March 2022

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