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CAHSEE Math 6.1 Statistics, Data, and Probability I 185 Views


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Statistics, Data, and Probability I: Drill Set 6, Problem 1. What is the likelihood of getting a 6 on the next roll?

Language:
English Language

Transcript

00:03

Here's a boring, unshmoopy question you'll find on some exam somewhere in your life...

00:08

Rolling a fair-numbered cube five times produced the following results: {1, 2, 3, 4, 5}.

00:15

What is the likelihood of getting a 6 on the next roll?

00:18

And here are the potential answers...

00:22

Total trick question.

00:23

It's really just asking for a probability -- that is,

00:26

what are the odds of getting a 6 on one roll of a 6 sided die?

00:31

Well, the answer is just 1 in 6.

00:33

But that's not all this problem is doing

00:35

-- it's illustrating the notion of dependence and independence in probability questions.

00:41

That is, any individual roll of a die is INDEPENDENT from any other.

00:49

So the fact that we got a 1, 2, 3, 4, and 5 on previous rolls

00:52

has NOTHING TO DO with the odds of getting a 6 on the next.

00:56

Quick example: A football stadium announcer

00:58

has all 64 thousand people stand and flip a normal coin.

01:03

32 thousand get heads. All the tails sit down.

01:06

They flip again. 16 thousand get a 2nd heads. The tails sit down.

01:10

They flip 24 more times leaving 1 guy who flipped heads EACH time.

01:16

That guy, of course, writes a book entitled HOW TO FLIP HEADS.

01:19

Chapter 4 is about humidity. Chapter 5 is about how to angle your thumb.

01:24

Chapter 6 is about posture...

01:26

Obviously, the guy is a scam artist. There was no method to his madness...

01:30

there just had to be somebody who would flip heads that many times in a row.

01:33

It's just random chance.

01:35

But then you've also got your dependent events.

01:38

Like... if we had a dozen cupcakes, and one of them had a human thumb in it.

01:42

The first guy to take a cupcake would have pretty good odds of avoiding that appendage...

01:47

...but once 8 people have gone and still no thumb...

01:49

...that 9th guy is going to be getting pretty nervous.

01:52

With four cupcakes left and one thumb he's got a one in four chance of...well...you know.

01:58

But we digress.

01:59

Our answer for this one is C... we're no more likely to roll a 6 than we are any other number.

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