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Statistics, Data, and Probability I Videos 30 videos

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Description:

Statistics, Data, and Probability I: Drill Set 5, Problem 3. If the Alpha Ape randomly selects a block, what is the probability that it is not triangularly or pentagonally shaped?

Language:
English Language

Transcript

00:03

Here's a shmoopy question for you...

00:05

Genetically modified apes are intent on building

00:08

weapons to reclaim the world they once dominated.

00:11

They are not monkeying around.

00:14

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

00:17

Their weapons are made from toy building blocks

00:19

so... the guards guffaw at their efforts.

00:23

In each set of blocks, there are:

00:26

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

00:29

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

00:32

and two hexagons. The witch apes love that one.

00:37

If the Alpha Ape randomly selects a block,

00:39

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

00:48

And here are the potential answers...

00:53

So what's this question really asking?

00:55

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

01:01

Notice that NOT in the question.

01:03

Not that kind of knot. This kind.

01:05

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

01:13

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

01:17

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

01:23

Think of it as looking like this:

01:29

So first we need to add up the TOTAL objects

01:32

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

01:36

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

01:44

So 12 is the denominator.

01:46

In the numerator we have whatever the total

01:48

of triangularly and pentagonally shaped items is --

01:51

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

01:55

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

01:58

a triangular or pentagonally shaped item.

02:01

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

02:05

It wants everything BUT those ape...

02:08

It wants everything BUT those shapes...

02:11

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

02:17

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

02:22

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

02:27

Thank you Jenny Craig.

02:28

Or answer B.

02:30

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

02:33

...the zookeeper arrives.

02:35

World domination will have to wait.

02:37

It's banana time. They have appeal.

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