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When 2 fair dice are rolled what is the probability of having 6 as sum

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When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 16 Jan 2010, 01:42
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When 2 fair dice are rolled what is the probability of having 6 as sum of the resulting numbers?

A 1/12
B 1/6
C 5/6
D 5/36
E 1/2
[Reveal] Spoiler: OA
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 16 Jan 2010, 02:02
lucalelli88 wrote:
when 2 fair dice are rolled what is the probability of having 6 as sum of the resulting numbers?
A 1/12
B 1/6
C 5/6
D 5/36
E 1/2

can you solve it.... because i got an answer but i cannot understand why it is wrong.


There are 36 possible outcomes when a pair of dice is rolled (6 for the first die X 6 for the second one). From this 36 outcomes five have a total of 6, {(1,5), (5,1), (2,4), (4,2), (3,3)}, hence the probability of the two numbers adding up to 6 is \(\frac{5}{36}\).

Answer: D.
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 16 Jan 2010, 02:41
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 16 Jan 2010, 03:36
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lucalelli88 wrote:
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?


When we count (4,2) and (2,4), it means that we get: 4 on die #1 and 2 on die #2 in first case and 2 on dies #1 and 4 on die #2 in the second case.

With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 16 Jan 2010, 05:35
thank you... my approach was wrong! KUDOS FOR YOU!


Bunuel wrote:
lucalelli88 wrote:
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?


When we count (4,2) and (2,4), it means that we get: 4 on die #1 and 2 on die #2 in first case and 2 on dies #1 and 4 on die #2 in the second case.

With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 12 Aug 2010, 18:43
Bunuel wrote:
With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.

well bit confused....
i think it means it is not times ie 1 time and 2nd time rather it is in 1st dice and in second dice...
but suppose if die we colored green and blue
would it be like
3 on G ,3 on B and 3 on B ,3 on G?

Can you please clarify?
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

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New post 13 Aug 2010, 02:03
frank1 wrote:
Bunuel wrote:
With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.

well bit confused....
i think it means it is not times ie 1 time and 2nd time rather it is in 1st dice and in second dice...
but suppose if die we colored green and blue
would it be like
3 on G ,3 on B and 3 on B ,3 on G?

Can you please clarify?


Not sure I understood your question...

There are only following 5 cases possible to have sum of 6:

#1|#2
1---5
2---4
3---3
4---2
5---1

Do we have any other case? It doesn't matter whether dice are colored, they are already numbered. (3,3) means 3 on die #1 and 3 on die #2 (3 on die #2 and 3 on die #1 is basically the same case).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: When 2 fair dice are rolled what is the probability of having 6 as sum   [#permalink] 13 Aug 2010, 02:03
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