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• 2010 AIME II Problems/Problem 13
  ...th higher numbered cards form another team. Let <math>p(a)</math> be the [[probability]] that Alex and Dylan are on the same team, given that Alex picks one of th [[Category:Intermediate Combinatorics Problems]]
  2 KB (328 words) - 11:15, 7 January 2021
• 2011 AMC 10A Problems/Problem 22
  ...th>E</math> and <math>D</math> have are less than 4.5. (There is a greater probability that <math>A</math>, <math>B</math>, and <math>B</math>, <math>C</math> are [[Category:Intermediate Combinatorics Problems]]
  14 KB (2,425 words) - 09:13, 5 November 2023
• 2011 AIME II Problems/Problem 12
  ...randomly select chairs at a round table that seats nine people. Let the [[probability]] that each delegate sits next to at least one delegate from another countr Use complementary probability and [[Principle of Inclusion-Exclusion]]. If we consider the delegates from
  5 KB (848 words) - 19:15, 30 April 2023
• 2011 AIME II Problems/Problem 15
  ...th> is chosen at random from the interval <math>5 \le x \le 15</math>. The probability that <math>\lfloor\sqrt{P(x)}\rfloor = \sqrt{P(\lfloor x \rfloor)}</math> i ...(\sqrt{621}-23)=\sqrt{61}+\sqrt{109}+\sqrt{621}-39,</cmath>which means the probability is <cmath>\frac{\sqrt{61}+\sqrt{109}+\sqrt{621}-39}{20}.</cmath>The request
  8 KB (1,273 words) - 14:03, 7 January 2023
• 1989 AHSME Problems/Problem 20
  ...een 100 and 200. If <math>\lfloor {\sqrt{x}} \rfloor = 12</math>, find the probability that <math>\lfloor {\sqrt{100x}} \rfloor = 120</math>. (<math>\lfloor {v} \ ...long segment, while the total possibilities region is 25 wide. Thus, the probability is
  1 KB (155 words) - 07:58, 22 October 2014
• Alcumus
  ...nerates high-quality solutions for the students to learn and to do similar problems easily. * Counting and [[Probability]]
  3 KB (533 words) - 10:55, 7 February 2023
• 1989 AHSME Problems/Problem 30
  ...ability is also <math>\frac{7\cdot 13}{20\cdot 19}</math>. Thus, the total probability of the two people being one boy and one girl is <math>\frac{91}{190}</math> [[Category: Intermediate Combinatorics Problems]]
  2 KB (293 words) - 17:13, 24 August 2020
• 2013 AIME I Problems/Problem 6
  ...ooks. If Melinda packs her textbooks into these boxes in random order, the probability that all three mathematics textbooks end up in the same box can be written ...ll be placed into the same box is <math>126+504+1260=1890</math>. So, the probability of this occurring is <math>\frac{(9\cdot7)(2+8+(4\cdot5))}{12\cdot11\cdot10
  5 KB (831 words) - 17:20, 9 January 2024
• 2014 AIME II Problems/Problem 2
  ...e risk factors, given that he has A and B is <math>\frac{1}{3}</math>. The probability that a man has none of the three risk factors given that he does not have r ...ath>x</math> be the number of men with all three risk factors. Since "the probability that a randomly selected man has all three risk factors, given that he has
  2 KB (371 words) - 15:19, 28 February 2022
• 2014 AIME II Problems/Problem 6
  ...d rolls it three times. Given that the first two rolls are both sixes, the probability that the third roll will also be a six is <math>\frac{p}{q}</math>, where < ...bility that he is using the biased die is <math>\frac{16}{17}</math>. The probability of rolling a third six is
  2 KB (356 words) - 09:03, 14 June 2021
• 2014 AIME II Problems/Problem 13
  ...shoe with a right shoe without regard to which shoes belong together. The probability that for every positive integer <math>k<5</math>, no collection of <math>k< ...ngs. Therefore, taking these cases out of a total of <math>10!</math>, the probability is <math>\frac{1}{10}+\frac{1}{50} = \frac{3}{25}</math>, for an answer of
  3 KB (509 words) - 15:33, 5 October 2023
• 2014 AIME I Problems/Problem 2
  ...h>N</math> blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is <math>0.58</math>. Find <math>N</m First, we find the probability both are green, then the probability both are blue, and add the two probabilities. The sum should be equal to <m
  1 KB (173 words) - 20:12, 15 January 2022
• 1993 AHSME Problems/Problem 24
  ...by one, pennies are drawn at random from the box and not replaced. If the probability is <math>a/b</math> that it will take more than four draws until the third So, probability for Case 1 to occur is:
  3 KB (558 words) - 00:25, 23 December 2020
• 1992 AHSME Problems/Problem 29
  ...urning up heads. If this coin is tossed <math>50</math> times, what is the probability that the total number of heads is even? Denote <math>P_n</math> as the probability that the number of heads is even. Then we have two cases:
  3 KB (472 words) - 19:29, 20 June 2021
• 1970 AHSME Problems/Problem 33
  ...>0000-9999</math>. We have <math>40000</math> digits and each has equal an probability of being <math>0,1,2....9</math>. [[Category: Intermediate Algebra Problems]]
  3 KB (418 words) - 15:54, 15 December 2018
• 1970 AHSME Problems/Problem 31
  ...e-digit numbers in which the sum of the digits is equal to 43, what is the probability that this number will be divisible by 11? [[Category: Intermediate Algebra Problems]]
  1 KB (172 words) - 10:53, 17 April 2022
• 2007 iTest Problems/Problem 19
  ...ail then <math>1</math> head is <math>\frac{1}{4}</math>. From there, the probability of getting <math>n</math> tails then <math>1</math> head is <math>\frac{1}{ [[Category:Intermediate Combinatorics Problems]]
  3 KB (397 words) - 01:18, 29 October 2023
• 2007 iTest Problems/Problem 21
  What is the probability that the value of the expression James wrote down is <math>7</math>? ...signs and minus signs between consecutive ones is <math>2^{14}</math>, the probability of getting a <math>7</math> is <math>\boxed{\textbf{(L) } \frac{1001}{2^{14
  2 KB (247 words) - 03:34, 14 June 2018
• 2007 iTest Problems/Problem 36
  ...n, m and n are two relatively prime positive integers such that m/n is the probability that the equation <math>x^4+25b^2=(4b^2-10b)x^2</math> has <math>\textit{at ...fore, in interval notation, <math>b \in [-17,0) \cup [5,17]</math>, so the probability that the equation has at least two distinct real solutions when <math>b</ma
  2 KB (276 words) - 15:49, 20 June 2018
• 2007 iTest Problems/Problem 42
  ...ming the stuntman is equally likely to land on any point in the field, the probability that he lands closer to the fence than to the flag pole can be written in s ...etry]], the square can be divided into four look-alike parts. To find the probability of landing closer to the fence, subtract the outlined red area from the are
  3 KB (524 words) - 23:01, 17 June 2018

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