Math Problems, Probability Problems

Problem of the Day: 2/26/13

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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