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ACT Math Pre-Algebra: Drill 3, Problem 4. Find the solution to this equation.
CAHSEE Math 4.1 Statistics, Data, and Probability I 213 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?
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.
Full Transcript
- 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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