## Articles and Excerpts, Volume 1 |

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AA Similarity ABCD American Mathematics Competitions angles Art of Problem blue marbles chosen at random Concept corresponding sides Counting & Probability diagram diﬀerent divisor of 200 divisors of 168 EFGH example Exercises for Section expected value exponent Figure ﬁnd ﬁrst ﬂip formula sheets geometric probability George Lenchner inﬁnitely integer International Mathematical Olympiad line segment Mandelbrot Competition Math Olympiad MATHCOUNTS Mathematical Olympiad Mathematical Talent Search natural number number of choices number of positive odd number outcomes region P(Area P(success parallel lines perfect square positive divisors positive integer prime factorization probability problems Problem 5.9 Problem Solving Bookstore Problem Solving Textbooks prove ratio real number Richard Rusczyk Sandor Lehoczky side length similar ﬁgures similar triangles Solution for Problem special points successful outcomes successful region There’s total number total outcomes traﬃc light triangles are similar USA Mathematical Olympiad USA Mathematical Talent USAMTS washer wins www.artofproblemsolving.com

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Page 9 - So the probability is number of favorable outcomes 125 total number of possible outcomes goo 36 KEY FACT O5: If an experiment is done two (or more) times, the probability that first one event will occur and then a second event will occur is the product of the probabilities. Example 10. A fair coin is flipped three times. What is the probability that the coin lands heads each time? SOLUTlON. When a fair coin is flipped: P(head) = - and P(tail) = - . By KEY FACT O5, P(3 heads) = P(head 1st time) x...

Page 26 - A line segment is broken at two random points along its length. What is the probability that the three new segments form a triangle?