Questions about the world of GRE Math from other sources and general math related questions.
rohanpshah
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5lb Book, Second Edition Chapter 23 Q20

by rohanpshah Sat Oct 10, 2015 1:16 pm

The question asks "A 6-sided cube has faces numbered 1 through 6. If the cube is rolled twice, what is the probability that the sum of the two rolls is 8?

The answer in the text is 5/36, but I think this is wrong. In particular, the answer suggests that the rolls that achieve a sum of 8 are (2,6), (3,5), (4,4), (5,3), and (6,2).

This misses off a "reverse" (4,4), such that the correct answer is 6/36, or 1/6. Please confirm that this is indeed an error in the book.
tommywallach
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Re: 5lb Book, Second Edition Chapter 23 Q20

by tommywallach Sat Oct 17, 2015 2:30 pm

Hey Rohan,

No, the book is correct. The mistake you're making is thinking you can "switch" 4 and 4. You can't. There's only ONE combo of 4 and 4, whereas there are two combos of 2 and 6, (2,6) and (6,2). This can be confusing to people, but it's true. In the 4 and 4 example, the first die and the second die are both 4. If you were to "switch" them, nothing would change: the first die and the second die would still both be 4. See the problem?

It could also help to think of this way. You know there are 36 ways to roll two dice. Let's list them out a bit:

1-1
1-2
1-3
1-4
1-5
1-6
2-1
2-2
2-3
...

See what happens? 1-1 is only listed twice, whereas both 1-2 and 2-1 are listed separately.

-t
rohanpshah
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Re: 5lb Book, Second Edition Chapter 23 Q20

by rohanpshah Mon Oct 19, 2015 5:02 am

I see - that makes sense. Many thanks!
tommywallach
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Re: 5lb Book, Second Edition Chapter 23 Q20

by tommywallach Fri Oct 23, 2015 7:06 pm

Glad to help!