A bowl contains three red, green, blue, and purple marbles. If Stefan draws out three marbles at random without replacement, what is the probability that all three marbles will be green?

*Solution to yesterday’s problem:*

If you were given this problem in, say, a Countdown Round at Mathcounts, you would probably realize that time is of the essence. So we need a way to quickly find the ratio of the two areas. Well, we could use an important principle in geometry: if the dimensions of any 2D shape are *cut in half*, then the area is **1/4 the original area**. Notice that the diameter of a small circle is half the diameter of the large circle. So one of the smaller circles is 1/4 the area of the bigger circle! Combining the two smaller circles, we find the ratio *1/2* to be our final answer.

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