Question

What is the probability of not rolling a 1-1 with a standard pair of dice?

Answer 1

The answers is 16/17 but I don't see how it makes any sense.

Answer 2

Better check that answer! There are 36 rolls with the combination of 2 dice. There is only one way to get 1-1.

35/36

Answer 3

Yes that's what I also got. It says 16/17 lol

Answer 4

Either the question is stated slightly differently, meaning something else. Otherwise, if that is what is truly the right question, then the answer is definitely off. I better know this from all the backgammon I play.

Answer 5

Even if we assume that the dice were indistinguishable, i.e. they were rolled simultaneously, even then we would have 18 combinations out of which only 1 combination would be 1-1. So the answer would be 17/18. I can't find a scenario in which the answer is 16/17.

Answer 6

"What is the probability of not rolling an 11 with a standard pair of dice? What is the complement of this event?"

This is the full question. I assumed that the '11' was referring to '1-1'

Answer 7

There are 36 rolls. All the doubles are unique. Rolls with 2 different numbers appear twice. 2-1 is still a "3" as is 1-2.

Answer 8

Yes, that's a different question. You can have 5-6 or 6-5.

34/36 = 17/18

Answer 9

Ya but if the dice were rolled one after another, the answer is 35/36. If they are rolled together I'm getting 17/18, where is the 16/17 lol.

Could it be referring to the sum of the numbers?

Answer 10

An "eleven" is the sum of the dice. You get that by rolling either a 5-6 or a 6-5. That's 2 rolls. What remains is 34 rolls for "not an eleven".

34/36 equals 17/18

Answer 11

yayayayaya so whererere is the 16/17 coming frommmmmmmmmmmmmm. arrghh

Answer 12

Is it possible that you are not copying down the question word-for-word? That can make all the difference in the world. Especially if substitute odds for probability or re-word something, or leave something out.

Answer 13

it's copied in verbatim. there is no mistakes.

Answer 14

Then:

The probability of "not rolling an eleven" with a standard pair of dice is unquestionably, absolutely, positively:

17/18

Answer 15

lol

Answer 16

imma google the question, maybe other people figured out where the 16/17 is coming from

Answer 17

Sometimes an answer key is wrong. THAT will cause grief!

Answer 18

it's possible but you see this is for my elearning course. I kind of doubt that there is a mistake. There certainly could be but it seems unlikely.

Answer 19

Don't even bother googling. If you expand the denominator from 17 to 34, it can't make sense. Because there are 36 rolls, not 34.

Answer 20

I'll email my teacher on the elearning course, let's see what he says about this. may be it is a mistake. I'm pretty sure that it is but let's see.

Answer 21

When I got a degree in math, long ago, I had a particular calculus book that had only ONE error in the answer key. I picked up a calc book 6 years ago and it was FULL of errors. A lot of publishers don't have time for proof-reading like they used to. Just because it's e-learning, that doesn't impress me about accuracy.

Answer 22

I agree with you @tcarroll010 but there is still a possibility that we are not seeing what the question is asking. I too agree with you that there is a mistake with the answer but there is still possibility that we aren't looking at the question correctly. So just to make sure, I've emailed the teacher, let's see what happens.

Answer 23

I'm not sure what "looking at the question correctly" means in this context. Math questions are notoriously "black-and-white". Especially easy ones. But it is very good to notify your teacher that the question or answer is definitely in error.

Answer 24

@tcarroll010 My teacher replied and he says that if you think the answer there is incorrect, then I should write my answer and a provide a reason for why its correct.

Answer 25

That's good direction from what sounds like a good teacher. He's basically just getting you to think.

Answer 26

But I still don't know whether the 11 is 1-1 or the sum of the rolled numbers. I asked him again and let's hope he replies with the answer this time. Will make things must easier to solve this problem.

Answer 27

Ok he says assume one after the other. @tcarroll010

Answer 28

What do you mean by "one after the other"? If you are suggesting that there is a difference between rolling the two dice together or rolling one die and then the other, the answer is the same.

Answer 29

No the answer wouldn't be the same as I don't know whether the 11 is a sum or 1-1 lol

Answer 30

That's the real question. What is 11? Is it eleven or two ones? It makes no difference whether or not you roll the two dice together or separately (one after the other). The only thing that matters is what is "11"? That is what the teacher should be telling you. I'm guessing that he doesn't have the entire problem in front of him.

Answer 31

I gave him the problem and showed where the problem is. Just waiting for a reply now...

Answer 32

As I mentioned before, I play a lot of tournament backgammon, which requires 2 dice, and believe me, we all know all the probabilities inside and out. And we would refer to "11" as eleven. So would a casino (all of them).

Answer 33

The thing is, you or any student should not have to guess at or interpret what a question like this means. Some questions are just poorly-worded. It's rare, but it happens. It could very well be that the person who framed the question is not strong in English.

Answer 34

So you're saying that 11 in backgammon is the sum of the rolled numbers?

Answer 35

Yes, without a doubt. A number associated with 2 dice is taken to mean the sum. Universally.

Answer 36

If the person who made up the question meant a roll of a "1" and another roll of a "1", he should write out

1-1 or "two" (spelled out like that)

to avoid ambiguity.

Writing "11" is VERY poor style. You can tell your teacher about this particular message, and I'm sure he would agree about the need to avoid ambiguity, especially this way.

Answer 37

In every dice game theory book I've read (I've read about 25), rolls of dice always have a dash between the 2 numbers. Sometimes they will spell out in a word the sum. For an eleven they will say eleven or 5-6 (implying the corresponding 6-5 also). They won't say 11 because that is definitely unclear.

Answer 38

no reply yet......i also emailed another student. let's hope one of them replies soon enough.

Answer 39

ya

Answer 40

So, currently, we are stuck with "11". but we can use that somewhat. In summary:

If they mean a "1" and a "1" -> P(not getting a "11") = 35/36

If they mean "eleven" -> P(not getting an "eleven") = 17/18

Those are our only possibilities. Either way, it's not 16/17

So we know there's a problem with the problem statement somewhere.

Answer 41

Anyway, I can't wait for your teacher to fix the problem, I have to go somewhere. When do you need some final answer? I can come back to this tomorrow for you. Does that work well with your schedule?

Answer 42

@tcarroll010 I just got the reply, it is actually 1-1. He said that on elearning activities it's written that way for some reason and he knows its confusing but the 11 should really be 1-1. So the problem is solved :D

Answer 43

So now that we know that one die rolls 1 and then the other rolls 1, there is 6 x 6 = 36 possible ways for this to have happened. Since there is just one way to get 1-1, there must be 35 ways to not get 1-1 hence the probability being 35/36. Do you agree?

Answer 44

Yes! You got it!

Answer 45

Well of course I got it. The only confusion was with the 11 lol. But thank you for your help.

@tcarroll010

Answer 46

uw! Nice working with you! @genius12