# Articles and Excerpts, Volume 1

AoPS Incorporated, 2006

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### Contents

 3 29 4 39 5 57
 6 85 Copyright

### Popular passages

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?
Page 46 - A positive integer is a perfect square if and only if it has an odd number of positive divisors.
Page 3 - Two marbles are randomly pulled from the bag at the | same time. What is the probability that both marbles are blue?