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

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Description:

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

Subjects:

Tags:

Statistics, Data Analysis, and Probability 6 / Independent and dependent events

Common Core Standards:

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.
Full Transcript