ShmoopTube

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Here's a shmoopy question for you...

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Genetically modified apes are intent on building

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weapons to reclaim the world they once dominated.

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They are not monkeying around.

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Unfortunately, they're not too hot at weapon-making.

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Their weapons are made from toy building blocks

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so... the guards guffaw at their efforts.

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In each set of blocks, there are:

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Three triangles, two squares, two rectangles, two circles,

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one pengaton -- the politically minded ape really loves that one;

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and two hexagons. The witch apes love that one.

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If the Alpha Ape randomly selects a block,

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what is the probability that it is not triangularly or pentagonally shaped?

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And here are the potential answers...

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So what's this question really asking?

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Well, it's a basic probability problem with one of those OR statements. And one curveball.

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Notice that NOT in the question.

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Not that kind of knot. This kind.

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It says "what is the probability that the selected toy is NOT triangularly OR pentagonally shaped?"

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The "Not" tells us that we're looking for... whatever follows it.

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Also note that the NOT covers BOTH triangularly AND pentagonally shaped objects.

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Think of it as looking like this:

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So first we need to add up the TOTAL objects

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at stake here -- as usual, that'll be the number we'll put in the denominator:

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And we get: 3 plus 2 plus 2 plus 2 plus one plus 2 for a total of 12 items.

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So 12 is the denominator.

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In the numerator we have whatever the total

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of triangularly and pentagonally shaped items is --

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and that's the quantity 3 plus 1 or 4.

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So we have 4 out of 12 as the odds of selecting

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a triangular or pentagonally shaped item.

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But ding ding ding -- this is the OPPOSITE of what the question is asking.

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It wants everything BUT those ape...

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It wants everything BUT those shapes...

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So the right answer is 12 MINUS that number or 8 and we get 8 over 12 as the odds of NOT

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selecting the triangular or pentagonally shaped weapons -- er um -- items from the box.

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And after going on a quick crash diet, our fraction reduces to 2 over 3.

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Thank you Jenny Craig.

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Or answer B.

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Before the Alpha Ape even has a chance to go block diving...

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...the zookeeper arrives.

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World domination will have to wait.

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It's banana time. They have appeal.

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