A box contains plain pencils and pens. A second box contains color pencils and crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?

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A box contains plain pencils and pens. A second box contains color pencils and crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?

Mathematics
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The first thought that comes to mind is that these two events are entirely independent of one another. This simplifies the calculation of probability. Without knowing the numbers of plain pencils and pens, or of colored pencils and crayons, we cannot find a numeric "answer." We could use the fact that drawing an instrument from one box and drawing another instrument from the other box are independent events to come up with a symbolic "answer" for the probability desired. Are you certain that there's not more to the question? perhaps an illustration?
A box contains 3 plain pencils and 9 pens. A second box contains 7 color pencils and 5 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
So much better, that there's no comparison! First box has 3 plain pencils and 9 pens, for a total of 12 instruments. Thus, the probability of picking a plain pencil from the first box is 3/12. OK with that?

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How many writing instruments are there in the 2nd box, total? How many of those are colored pencils? What is the probability of drawing a colored pencil from the 2nd box?
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The probability of selecting a colored pencil from the second box is 7/12. Multiply that by 3/12 from the first box, and you get 21/144, or 7/48.

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