Each of two boxes contains three chips numbered $$1$$, $$2$$, and $$3$$. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even? (2015 AMC 8 Problem, Question \#7) 
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We can instead calculate the probability that their product is odd, and subtract this from $$1$$. In order to get an odd product, we have to draw an odd number from each box. We have a $$\frac23$$ probability of drawing an odd mumber from one box, so there is a $$\left(\frac{2}{3}\right)^{2}= \frac{4}{9}$$ probability of having an odd product. Thus, there is a $$1- \frac{4}{9}= \frac{5}{9}$$ probability of having an even product. 