ShmoopTube

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

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Good luck with this one.

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

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

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The possible outcomes are shown in the table below.

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

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And here are the potential answers...

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OK, what's this question asking?

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Well, it's a matrix style question.

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

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

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We calculate the odds of BOTH or EITHER event happening.

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

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

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an A and an E.

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

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

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Now for the second.

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

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

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

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How do we get the totals? We just multiply.

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

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

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

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Here here here here here and here...

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

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25 -- in the denominator makes sense.

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

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

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