ShmoopTube

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

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Kerry rolls a fair-numbered cube twice.

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The possible outcomes are shown in the following tree diagram.

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

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And here are the potential answers:

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OK, so what's this question asking?

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

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Is that a cube that doesn't cheat?

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

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or pips that represent those numbers...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Choice B.

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Unfortunately, this story has a sad ending...

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

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

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