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When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]
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16 Jan 2010, 02:42
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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
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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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16 Jan 2010, 03:02
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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16 Jan 2010, 03:41
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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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16 Jan 2010, 04:36
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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16 Jan 2010, 06:35
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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12 Aug 2010, 19:43
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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13 Aug 2010, 03:03
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 15 24 33 42 51 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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Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]
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14 Aug 2017, 03:34
Bunuel wrote: 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 15 24 33 42 51 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). In such a case, 1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same. So our possible outcomes are just 30. Our answer would then be 1/6. Am i missing something?



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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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14 Aug 2017, 03:48
nkimidi7y wrote: 1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same.
So our possible outcomes are just 30.
Our answer would then be 1/6.
Am i missing something? No, there are till 36 cases: (1, 1) (1, 2) ... (1, 6) 6 cases. (2, 1) (2, 2) ... (2, 6) 6 cases. (3, 1) (3, 2) ... (3, 6) 6 cases. (4, 1) (4, 2) ... (4, 6) 6 cases. (5, 1) (5, 2) ... (5, 6) 6 cases. (6, 1) (6, 2) ... (6, 6) 6 cases. 6*6 = 36.
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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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15 Aug 2017, 06:36
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nkimidi7y wrote: In such a case, 1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same.
So our possible outcomes are just 30.
Our answer would then be 1/6.
Am i missing something?
Don't think of it like combination choices where you can flip and come up with the same thing. Think of 36 possibilities in 6 groups where first roll is 1 for all pairs in row 1, 2 for all pairs in row 2 and so on. You have 5 bold faced choices that have sum 6. Every row starting 15 has one matching pair where sum is 6, but the last row starting with 6 cannot come up with any second dice roll number to get to a sum of 6. So we only have 5 of 36 choices that have a sum of 6. 11,12, 13,14, 15,16 21,22,23, 24,25,26 31,32, 33,34,35,36 41, 42,43,44,45,46 51,52,53,54,55,56 61,62,63,64,65,66
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum
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