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# What is the probability that the sum of two dice will yield

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Intern
Joined: 07 Feb 2012
Posts: 35
GMAT 1: 730 Q45 V45
GPA: 3.81
WE: Consulting (Consulting)
What is the probability that the sum of two dice will yield  [#permalink]

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08 Feb 2012, 13:50
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83% (00:36) correct 17% (00:30) wrong based on 11 sessions

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What is the probability that the sum of two dice will yield a 4 or a 6?

The # of ways to get a 4: 1 and 3, 2 and 2, 2 and 2, 3 and 1
The # of ways to get a 6: 1 and 5, 2 and 4, 3 and 3, 3 and 3, 4 and 2, 5 and 1
Total of 10
Total possible outcomes = 6 x 6 = 36, therefore the probability is 10/36

This is in the MGMAT book on word translations, page 93. It says the answer is 8/36 because it does not count 2 and 2 and 3 and 3 twice (but it does view 3 and 1 and 1 and 3 as different, likewise it considers 1 and 5 and 5 and 1 different and it considers 2 and 4 and 4 and 2 to be different)

Why does it not count those twice? It is possible to get 2 and 2 two different ways and 3 and 3 two different ways so I thought you needed to account for that.
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Joined: 02 Sep 2009
Posts: 64144
Re: What is the probability that the sum of two dice will...  [#permalink]

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08 Feb 2012, 14:11
3
What is the probability that the sum of two dice will yield a 4 or a 6?

The # of ways to get a 4: 1 and 3, 2 and 2, 2 and 2, 3 and 1
The # of ways to get a 6: 1 and 5, 2 and 4, 3 and 3, 3 and 3, 4 and 2, 5 and 1
Total of 10
Total possible outcomes = 6 x 6 = 36, therefore the probability is 10/36

This is in the MGMAT book on word translations, page 93. It says the answer is 8/36 because it does not count 2 and 2 and 3 and 3 twice (but it does view 3 and 1 and 1 and 3 as different, likewise it considers 1 and 5 and 5 and 1 different and it considers 2 and 4 and 4 and 2 to be different)

Why does it not count those twice? It is possible to get 2 and 2 two different ways and 3 and 3 two different ways so I thought you needed to account for that.

(3, 1) means that you got 3 on the first die and and 1 on the second die, which is different from (1, 3): getting 1 on the first die and and 3 on the second die. Now, (3, 3) means getting 3 on the first die and 3 on the second, which is exactly the same as getting getting 3 on the second die and 3 on the first die.

So, # of favorable outcomes is:
Sum of 4: (1, 3), (3, 1), and (2, 2) --> 3 outcomes;
Sum of 4: (1,5), (5, 1), (2,4), (4, 2), and (3,3) --> 5 outcomes;

Total # of outcomes is 6*6=36;

P=(3+5)/36=8/36.

Hope it's clear.
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Intern
Joined: 07 Feb 2012
Posts: 35
GMAT 1: 730 Q45 V45
GPA: 3.81
WE: Consulting (Consulting)
Re: What is the probability that the sum of two dice will yield  [#permalink]

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08 Feb 2012, 16:20
Perfect explanation, I get it now. Thanks!
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Re: What is the probability that the sum of two dice will yield  [#permalink]

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21 Jun 2016, 10:06
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Re: What is the probability that the sum of two dice will yield   [#permalink] 21 Jun 2016, 10:06