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# When two dice are rolled, what is the probability that the difference

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Math Expert
Joined: 02 Sep 2009
Posts: 50036
When two dice are rolled, what is the probability that the difference  [#permalink]

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09 Mar 2016, 13:04
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Difficulty:

35% (medium)

Question Stats:

61% (01:21) correct 39% (01:24) wrong based on 147 sessions

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When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

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Joined: 12 Dec 2015
Posts: 18
Re: When two dice are rolled, what is the probability that the difference  [#permalink]

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09 Mar 2016, 14:06
1
We have 8 outcomes that satisfy the question:

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

For the first, second, fifth and sixth pairs the probability is (1/6*1/6)*4= 4/36. For fifth and sixth pairs probability is (1/6*2/6)*2=4/36, and the sum of all possibilities is 4/36+4/36=8/36=2/9

I think the answer is B
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Re: When two dice are rolled, what is the probability that the difference  [#permalink]

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10 Mar 2016, 21:36
3
Hi AlexIV,

Your work here is perfect, but it looks like you did a bunch of 'extra' math that wasn't necessary.

When you roll two 6-sided dice, there are (6)(6) = 36 possible outcomes. Once you listed the 8 options that 'fit' what the question was looking for, all you had to do was reduce the fraction:

8/36 = 2/9

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 06 Feb 2016 Posts: 1 Re: When two dice are rolled, what is the probability that the difference [#permalink] ### Show Tags 28 Mar 2016, 05:59 1 I found it easiest to make a quick chart, it took about 1 min If the top horizontal row is the first die and the first vertical row the second die then, the difference between the two is the result in the number chart. I just counted the 2s to avoid missing any and then since it is 6x6 for all possible outcomes, then 8/36 is the answer. Hence 2/9 - 123456 1 012345 2 101234 3 210123 4 421012 5 532101 6 643210 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12694 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: When two dice are rolled, what is the probability that the difference [#permalink] ### Show Tags 28 Mar 2016, 11:07 2 Hi cecammiade, That type of 'brute force' approach is perfect for certain types of questions on Test Day. As you've pointed out, it didn't take much time or effort to do the work and THAT is something to keep in mind as you're working through the entire GMAT. Most GMAT questions can be solve in a variety of ways, so sometimes you just have to put the pen on the pad and quickly 'map out' the solution. Your willingness to think in those terms likely means that you have a high potential to score well on Test Day. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: When two dice are rolled, what is the probability that the difference  [#permalink]

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29 Mar 2016, 01:42
Bunuel wrote:
When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

Total Outcomes = 6*6 = 36

Favorable outcomes = {1, 3}, {2, 4}, {3, 5}, {3, 1}, {4, 6}, {4, 2}, {5, 3}, {6, 4} = 8 cases

Probability = Favorable Outcomes / Total Outcomes = 8/36 = 2/9

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Re: When two dice are rolled, what is the probability that the difference  [#permalink]

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03 May 2016, 04:23
Probability = Favorable outcomes / Total outcomes
Possible Favorable outcomes = (1,3) , (2,4) , (3,5) , (4,6) , (3,1) , (4,2) , (5,3) , (6,4)
Number of possible outcomes = 8
Total outcomes = 6 * 6 = 36

Probability = $$\frac{8}{36}$$ = $$\frac{2}{9}$$
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Re: When two dice are rolled, what is the probability that the difference  [#permalink]

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26 Oct 2017, 15:25
Bunuel wrote:
When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled. Of the 36 possible outcomes, there are 8 outcomes with a difference of 2: (1,3), (3,1), (2,4), (4,2), (3,5), (5,3), (4,6), (6,4). So, the probability of getting the difference of 2 is 8/36 = 2/9.

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Re: When two dice are rolled, what is the probability that the difference &nbs [#permalink] 26 Oct 2017, 15:25
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