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# Two identical dice are rolled together. If the sum of the dice is 7

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Math Expert
Joined: 02 Sep 2009
Posts: 45374
Two identical dice are rolled together. If the sum of the dice is 7 [#permalink]

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29 Jan 2018, 05:40
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Difficulty:

25% (medium)

Question Stats:

57% (00:47) correct 43% (00:26) wrong based on 64 sessions

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Two identical dice are rolled together. If the sum of the dice is 7, what is the probability that one of the numbers showing is a 4?

(A) 1/36
(B) 1/18
(C) 1/6
(D) 11/36
(E) 1/3

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Two identical dice are rolled together. If the sum of the dice is 7 [#permalink]

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29 Jan 2018, 06:12
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KUDOS
Bunuel wrote:
Two identical dice are rolled together. If the sum of the dice is 7, what is the probability that one of the numbers showing is a 4?

(A) 1/36
(B) 1/18
(C) 1/6
(D) 11/36
(E) 1/3

When two dice are rolled together the various ways we can
get a sum of 7 are (1,6),(2,5),(3,4),(4,3),(5,2), and (6,1)

There are a total of 6 possibilities when the sum is 7, and 2 of them need a 4.
Therefore, the probability of one of the numbers showing is a 4 is $$\frac{2}{6} = \frac{1}{3}$$ (Option E)
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Re: Two identical dice are rolled together. If the sum of the dice is 7 [#permalink]

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30 Jan 2018, 11:19
Bunuel wrote:
Two identical dice are rolled together. If the sum of the dice is 7, what is the probability that one of the numbers showing is a 4?

(A) 1/36
(B) 1/18
(C) 1/6
(D) 11/36
(E) 1/3

The number of ways to obtain a sum of 7 when two dice are rolled is:

1,6 or 6,1
2,5 or 5,2
3,4 or 4,3

So, there are 6 total ways to obtain a sum of 7, and, of those ways, there are two outcomes in which a 4 is showing, so the probability is 2/6 = 1/3.

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Re: Two identical dice are rolled together. If the sum of the dice is 7 [#permalink]

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31 Jan 2018, 05:09
Bunuel wrote:
Two identical dice are rolled together. If the sum of the dice is 7, what is the probability that one of the numbers showing is a 4?

(A) 1/36
(B) 1/18
(C) 1/6
(D) 11/36
(E) 1/3

Solution

• Two dices are rolled and a sum of 7 is obtained.
o We can get a sum of 7 in the following ways.
 (1,6) (6,1)
 (5,2) (2,5)
 (4,3) (3,4)
o Thus, total possible cases of getting a sum of seven = 6
• We need to find out in how many cases can one of the dices show a 4.
o From the cases shown above, we can clearly see that the total cases with 4 on one of the dices = 2
• Thus, the required probability = Favorable Cases/Total Cases = $$\frac{2}{6} = \frac{1}{3}$$

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Saquib
Quant Expert
e-GMAT
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Re: Two identical dice are rolled together. If the sum of the dice is 7   [#permalink] 31 Jan 2018, 05:09
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