Can someone explain to me why the probability is 1/11?

Question

Setup: We are rolling two dice. We know at least one of the dice shows a six? What is the probability that the sum of the two rolls is 12?

Why is the answer 1/11?

Thanks,
Kevin

Please stop telling me it's 1/6. It isn't. If you think it is, please spare both me and you the time by not answering. Also if you could somehow use conditional probability to explain it, that would be great.

Thanks,
Kevin

Answer 1

Hi Kevin. Wherever you got your answer, it is right. People are answering semantically a different question than what you are asking here.

You are rolling 2 dice. There are 36 possible combinations that you can come up with from rolling 2 dice. They are listed below. Assume for this explanation that the first number is Die 1 and the second number is the result of Die 2.

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

These are the 36 possibilities. When you are told that you have at least one 6, then you are looking at only the 11 possibilities that have a 6 in them. These would be 16, 26, 36, 46, 56, 66, 61, 62, 63, 64, 65. Note that 16 and 61 are not the same event. Of these 11 roll combinations that have a 6 in it...only the 6-6 totals 12. Therefore 1 out of 11 times will the total of 2 dice be 12 when you are told that you have at least one 6 already.

If this is in some way doesn't make sense, feel free to e-mail me.

Answer 2

Hey Kevin, I'm getting 2/11, not 1/11, and I'll explain why. We know that there are 36 equally likely possible outcomes from throwing 2 dices. Out of those, 11 of them has at least 1 six showing. But 2 out of those 11 has five as the other number showing. So I'm not sure why you say it's 1/11? And I don't understand the other folks here either, if we just ask, "What's the odds of throwing a sum of 11 with a pair of dice?", the answer is 2 out of 36, or 1/18, not 1/12, and not 1/6.

Answer 3

Well, there are 6 sides on each die, making 12 sides between the two. You know that one of them is a six, but you don't know which, leaving 11 more sides that could be the second number. For the sum to be 12, you'd have to have another 6. Since one die is already showing a six, there's only one chance out of all 11 that the other number will be a 6, and therefore there's a 1/11 chance that the sum is 12.

Sorry if that's confusing.

Answer 4

Since you are rolling 2 dice, and you know one of them will be a 6, there are 11 faces left on the dice. However, you can only get one six from these 11 faces.

Therefore, the probablity is 1/11.

Answer 5

Because each die has 6 sides, so that makes 6 possibilities per die. But since you already know for sure one is already a 6, that takes away one possibility, making it 11. Oh and the only way you can get 12 with 6 is to get 6 and 6, so there is only 1 way to get 6 on the other die, which makes it 1. Does that make sense?

Answer 6

Because you are rolling a 11 sided die. The chance of getting a 6 of the next roll if 1/11

Your question makes it sound like you are rolling two six sided dice twice, which would be:

6 + x + y + z = 12

x + y + z = 6

Since x,y, and z are integers between 1 and 6:

(1,1,4),(1,2,3),(1,3,2),(1,4,1)
(2,1,3),(2,2,2),(2,3,1)
(3,1,2),(3,2,1)
(4,1,1)

Are our only options. Ten of them.

Then you have to find out how many rolls are there total.

Let's let this up in base 5, which has six numbers, between 000-555. Between and including 000 and 555 in base 5, there are 1000 numbers. 1000 in base 5 = 5^3 in base ten which equals 125. Meaning we have 125 different rolls that we could have.

10/125

Answer 7

it shouldn't be 1/11.... i'm pretty sure it should be 1/6. After getting a six already, there's only one more die to roll. There are only six numbers, meaning that there's a 1 in 6 chance it'll be another six..

Answer 8

there are 36 combinations, how many combinations make 12? a 6 and a 6....that means that the probability is 1/36...I'm not sure what kind of dice you are using, they should be 6 sided...

Answer 9

well depends on the type of dice I suppose?

using six sided dice, it wouldnt be 1/11...

Answer 10

The answer isn't 1/11

It would be 1/6