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

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Bunuel
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When two dice are rolled, what is the probability that the difference [#permalink] New post   09 Mar 2016, 13:04
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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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B
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AlexIV
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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   09 Mar 2016, 14:06
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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] New post   10 Mar 2016, 21:36
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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

Final Answer:
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B


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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   28 Mar 2016, 05:59
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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
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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   28 Mar 2016, 11:07
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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.

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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   29 Mar 2016, 01:42
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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

Answer: Option B
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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   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 = \(\frac{8}{36}\) = \(\frac{2}{9}\)
correct answer - B
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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   26 Oct 2017, 15:25
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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.

Answer: B
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Re: When two dice are rolled, what is the probability that the difference [#permalink] New post   08 Oct 2022, 09:32
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Given that Two dice are rolled and we need to find What is the probability that the difference between the two numbers is 2?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Lets start listing down the cases where the difference between the two numbers is 2. Following are the possible cases
(1,3)
(2,4)
(3,1), (3,5)
(4,2), (4,6)
(5,3)
(6,4)

=> 8 cases

=> Probability that the difference between the two numbers is 2 = \(\frac{8}{36}\) = \(\frac{2}{9}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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Re: When two dice are rolled, what is the probability that the difference [#permalink]
08 Oct 2022, 09:32
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