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  • ...tofproblemsolving.com/store/item/intro-counting Introduction to Counting & Probability] * [https://artofproblemsolving.com/store/item/intermediate-algebra Intermediate Algebra]
    5 KB (658 words) - 09:03, 3 November 2024
  • * Intermediate is recommended for students who can expect to pass the AMC 10/12. ==== Intermediate ====
    24 KB (3,198 words) - 19:44, 4 December 2024
  • Patrick is the author of the ''Introduction to Counting & Probability'' textbook and solutions manual, published by AoPS in 2005, and more genera ...fproblemsolving.com/Books/AoPS_B_Item?page_id=3 Introduction to Counting & Probability]''
    3 KB (379 words) - 10:18, 27 September 2024
  • * Intermediate is recommended for students grades 9 to 12. ==== Intermediate ====
    7 KB (901 words) - 13:11, 6 January 2022
  • ...metic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], and [[probability]] and other secondary school math topics. Problems are designed to be solv * [http://www.artofproblemsolving.com/Store/viewitem.php?item=interm:algebra Intermediate Algebra] by [[Richard Rusczyk]] and [[Mathew Crawford]].
    4 KB (529 words) - 08:01, 24 July 2024
  • ...metic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], and [[probability]] and other secondary school math topics. Problems usually require either ...but feel they lag behind in their understanding of basic combinatorics and probability relative to their other areas of math. [http://www.artofproblemsolving.com
    8 KB (1,067 words) - 19:15, 24 October 2024
  • ...such as [[algebra]], [[geometry]], [[number theory]], [[counting]], and [[probability]]. .../Prealgebra 1 | Prealgebra 1]] — [https://artofproblemsolving.com/school/course/catalog/prealgebra1 Details] ([https://artofproblemsolving.com/store/item/p
    8 KB (965 words) - 02:41, 17 September 2020
  • ...Examples include the [[Monty Hall paradox]] and the [[birthday problem]]. Probability can be loosely defined as the chance that an event will happen. == Introductory Probability ==
    4 KB (590 words) - 10:52, 28 September 2024
  • ...counting is often a far simpler approach. A large hint that complementary counting may lead to a quick solution is the phrase "not" or "at least" within a pro ...rmally, if <math>B</math> is a [[subset]] of <math>A</math>, complementary counting exploits the property that <math>|B| = |A| - |B^c|</math>, where <math>B^c<
    8 KB (1,192 words) - 16:20, 16 June 2023
  • ...f the four adjacent vertices, each with equal [[probability]]. What is the probability that no two ants arrive at the same vertex? ...ants can do their desired migration, and then multiply this number by the probability that each case occurs.
    10 KB (1,840 words) - 14:01, 4 July 2024
  • == Intermediate topics in combinatorics == * [[Geometric probability]]
    910 bytes (77 words) - 15:23, 18 May 2021
  • ...h>1</math>'s. If a number is chosen at random from <math> S, </math> the [[probability]] that it is divisible by <math>9</math> is <math> p/q, </math> where <math The probability is <math>\frac{133}{780}</math>, and the answer is <math>133 + 780 = \boxed
    8 KB (1,283 words) - 18:19, 8 May 2024
  • ...- and are sent off to slay a troublesome dragon. Let <math>P</math> be the probability that at least two of the three had been sitting next to each other. If <mat We can use [[complementary counting]], by finding the probability that none of the three knights are sitting next to each other and subtracti
    9 KB (1,464 words) - 10:50, 30 October 2024
  • ...g at the sequences which have one digit repeated twice, we notice that the probability that the sequence starts with 1 is <math>\frac{1}{10}</math>. This means we ==Solution 3 (Complementary Counting)==
    5 KB (855 words) - 19:26, 14 January 2023
  • ...being equally likely. Let <math>\frac m n</math> in lowest terms be the [[probability]] that no two birch trees are next to one another. Find <math>m+n</math>. ...ave them each in their own category, but in the end it will not change the probability of the birch trees being near each other. That is, in the end, you multiply
    7 KB (1,115 words) - 23:52, 6 September 2023
  • ...including letter 9, there are <math>k+2</math> places to insert letter 9, counting the possibility of not having to insert it (i.e., if it arrived before lunc This problem is very similar to AoPS Intermediate Counting and Probability problem 4.8(which is another AIME problem but I don't know which one)
    7 KB (1,188 words) - 07:02, 15 August 2024
  • ...math> times. Let <math>\frac{i}{j}^{}_{}</math>, in lowest terms, be the [[probability]] that heads never occur on consecutive tosses. Find <math>i+j_{}^{}</math> ...of <math>2^{10}</math> possible flips of <math>10</math> coins, making the probability <math>\frac{144}{1024} = \frac{9}{64}</math>. Thus, our solution is <math>9
    3 KB (427 words) - 14:03, 24 June 2024
  • ...that, when two socks are selected randomly without replacement, there is a probability of exactly <math>\frac{1}{2}</math> that both are red or both are blue. Wha ...ber of red and blue socks, respectively. Also, let <math>t=r+b</math>. The probability <math>P</math> that when two socks are drawn randomly, without replacement,
    7 KB (1,328 words) - 19:24, 5 February 2024
  • ...t, right, up, or down, all four equally likely. Let <math>p</math> be the probability that the object reaches <math>(2,2)</math> in six or fewer steps. Given th ...>\frac{4!}{2!2!} = 6</math> ways for these four steps of occuring, and the probability is <math>\frac{6}{4^{4}}</math>.
    3 KB (602 words) - 22:15, 16 June 2019
  • ...gular [[octahedron]] so that each face contains a different number. The [[probability]] that no two consecutive numbers, where <math>8</math> and <math>1</math> ...t and finish at specified vertices, can be done in only 2 ways. Since this counting method treats each path as different from its reverse, there are <math>8\cd
    11 KB (1,836 words) - 20:08, 26 August 2024

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