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Each block in a certain bucket is either red, yellow, or blue. There are half as many red blocks as blue blocks and 3 times as many yellow blocks as red blocks. If a block is withdrawn from the bucket at random, what is the probability that the block is blue?
Since the problem reference unknown values and asks to know the distribution of said values, plugging in an easy number is a very viable tactic. In this case, we first want to locate the foundation variable dictating all aspects of the problem. Here, we see that the blue blocks dictate the red, which in turn dictate the yellow. So, plug in an easy value for the blue blocks such as blue = 4.
If there are 4 blue, and half as many red as blue, then there are 2 red blocks. Finally, if there are three times as many yellow as red blocks, then there are 6 red blocks.
Now, to determine the probability of selecting a blue block, remember that probability is defined as desired possibilities / total possibilities. In this case, there are 4 desired blue blocks out of a total of 4 + 2 + 6 = 12 blocks. Therefore, the probability of selecting a blue is 4/12 or 1/3, so select choice B.
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