2
Part of 2014 AIME Problems
Problems(2)
Balls and Urns
Source: 2014 AIME I Problem 2
3/14/2014
An urn contains green balls and blue balls. A second urn contains green balls and blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is . Find .
probabilityratioalgebralinear equationAMC
Health Risk Factors Probability Problem
Source: 2014 AIME II Problem 2
3/27/2014
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C. within a population of men. For each of the three factors, the probability that a randomly selected man in the population as only this risk factor (and none of the others) is 0.1. For any two of the three factors, the probability that a randomly selected man has exactly two of these two risk factors (but not the third) is 0.14. The probability that a randomly selected man has all three risk factors, given that he has A and B is . The probability that a man has none of the three risk factors given that he does not have risk factor A is , where and are relatively prime positive integers. Find .
probabilitynumber theoryrelatively primeAMC