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Description:

Statistics, Data, and Probability I: Drill Set 5, Problem 4. What is the probability that the pointer creates a new winner?

Language:
English Language

Transcript

00:03

Here's a shmoopy question for you...

00:06

The following fair spinner is spun one time.

00:09

According to Norse legend, God spins it every time a new human child is born,

00:14

to determine whether they're going to be a winner... or a loser.

00:18

Aw, and you thought we had free will.

00:21

What is the probability that the pointer creates a new... winner?

00:24

And here are the potential answers...

00:29

OK, that FAIR spinner thing again.

00:31

For these kinds of problems, FAIR just means that what you see is what you get...

00:35

...that is, the drawing is drawn to scale and the spinner isn't a Las Vegas scam to

00:39

cheat widows out of their savings by always landing on LOSE.

00:43

It's an odds or probability question -- but it's kind of a trick question as well.

00:47

Just look at the wheel. The total real estate taken up by "WIN" is ... large.

00:52

Like... "clearly over half" large.

00:54

Now look at the answers. Anything, uh.. stand out?

00:58

Yeah -- it's D.

00:59

No other answer could POSSIBLY work. It's D. We can just click it and move on.

01:04

Go ahead. Don't be shy. There's nothing wrong with using common sense.

01:07

BUT let's assume for a second that we actually want to learn how to solve this problem...

01:12

If we really wanted to get fancy, there's a few big fat clues here,

01:15

the biggest of which is the presence of right angle.

01:19

We know that a right angle is 90 degrees and

01:21

is a quarter of a circle... or 25% of it.

01:25

And that right angle is bisected with this line. That is, it's cut in half.

01:30

So each of these tiny slices is 12.5% of the circle or 45 degrees.

01:35

We have 3 LOSES of 12.5% which total to 37.5%.

01:40

The wins then have to be 100-37.5% or 62.5%.

01:45

We made the calculation but... we really didn't have to.

01:48

In fact, wasting so much time makes us feel like a real loser.

01:53

Wait a minute...

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