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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?
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.
Full Transcript
- 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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