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CAHSEE Math 4.1 Statistics, Data, and Probability I 214 Views


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Description:

Statistics, Data, and Probability I: Drill Set 4, Problem 1. What is the probability of obtaining both a vowel and an odd number?

Language:
English Language

Transcript

00:03

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

00:07

Good luck with this one.

00:09

Two fair spinners, each separated into equal regions, one with the letters A through E

00:13

on it, and the other with numbers 1 through 5, are spun.

00:20

The possible outcomes are shown in the table below.

00:24

What is the probability of obtaining both a vowel and an odd number?

00:29

And here are the potential answers...

00:36

OK, what's this question asking?

00:38

Well, it's a matrix style question.

00:45

Matrix questions are common on exams and they all do more or less the same thing --

00:52

first one event must happen; then a second event happens.

00:58

We calculate the odds of BOTH or EITHER event happening.

01:02

In this case, the first CONDITION requires us to have a vowel.

01:07

If we look across the top layer we see that there are only 2 vowels there --

01:11

an A and an E.

01:13

So if we don't land on the A or the E... we're going to be outta luck.

01:17

Our first spin has a 2 out of 5 likelihood of hitting our mark.

01:26

Now for the second.

01:28

If we DO roll an A, what then are our odds of spinning an ODD number?

01:34

Well, there are 3 odd numbers... 1, 3 and 5.

01:36

So we have a 3 out of 5 shot at rolling 'em along with either an A or an E.

01:41

How do we get the totals? We just multiply.

01:43

So that's 2 over 5 for the vowel TIMES 3 over 5 for the odd number... and we get 6 over 25.

01:50

And if we really got stuck, we could just use the old brut force method...

01:55

...and just circle all the winners...

01:56

Here here here here here and here...

02:00

...putting those 6 in the numerator and putting the total number of possibilities --

02:03

25 -- in the denominator makes sense.

02:07

So our answer is D... six-twenty-fifths.

02:11

Now that you're a master spinner, you can really impress everyone else in your afternoon spin class.

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