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CAHSEE Math 3.5 Statistics, Data, and Probability I 205 Views


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Statistics, Data, and Probability I: Drill Set 3, Problem 5. What is the probability that the sum of the two rolls adds up to 9?

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Transcript

00:03

Here's an unshmoopy question you'll find on an exam somewhere, somewhere in life...

00:07

Kerry rolls a fair-numbered cube twice.

00:11

The possible outcomes are shown in the following tree diagram.

00:14

What is the probability that the sum of the two rolls adds up to 9?

00:20

And here are the potential answers:

00:27

OK, so what's this question asking?

00:29

Well, first we have to know what a "fair numbered cube" is, right?

00:33

Is that a cube that doesn't cheat?

00:36

Nah... it's just a $5 word for a die. That is, it has numbers 1 through 6 on it...

00:42

or pips that represent those numbers...

00:45

...and its... fair. That is, each number has the same odds of being rolled.

00:50

There are a few ways of getting to the right answer but let's start with the brute force

00:53

method and quickly list all of the possibilities -- check 'em out here:

00:59

The visual chart they give us can easily get us to the right answer if we just manually

01:03

add the numbers to get all the 9s -- so let's note the circled numbers.

01:08

Some easy observations help speed us to our answer here -- first, if we roll a 1 or a

01:13

2 on the first roll, we'll NEVER get to a 9 so we can just... throw 'em out.

01:20

We have a TOTAL of 36 possible rolls here. So all we have to do is hunt through the remaining

01:25

rolls and add up how many combinations get us to 9.

01:28

That is... if we roll a 3 on the first roll,

01:31

the way we get to a 9 is by having the second roll be a 6.

01:35

If the first roll is a 4, we need a 5 to get there. And... so on --

01:38

So we have: A first roll of 3 plus a 6 A first roll of 4 plus a 5

01:43

A first roll of 5 plus a 4 And a first roll of 6 plus a 3

01:48

So there we go. Four possible ways of making a 9 with two rolls...

01:53

...or a 4 out of 36 chance of making a 9 on two rolls.

01:57

Four-thirty-sixths simplifies to one-ninth... or a bit over 10%.

02:01

All we're really concerned about though... is that we found our answer.

02:05

Choice B.

02:06

Unfortunately, this story has a sad ending...

02:09

...as it turns out Kerry was too young to be gambling.

02:12

Hang on, Kerry. We'll get you a good lawyer.

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