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SAT Math 1.3 Statistics and Probability. Approximately what is the probability that they will be placed in alphabetical order?
SAT Math 1.4 Statistics and Probability. If two standard 6-sided dice are rolled, what is the probability that the sum of the dice will be gre...
SAT Math 1.5 Statistics and Probability. If Silas draws one card, then places it in his pocket and draws another, what is the probability that...
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?
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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