# Dice pls help need answer

#### Alex919191

##### New member
on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible

#### Dr.Peterson

##### Elite Member
What do you think about it? We want to work with you, helping you to think through it on your own, and for that, we need to know where you are coming from. (And don't forget that "in your own words" means your words, not ours! This is meant to be a chance for you to think for yourself, not just to get someone else to think.)

#### Alex919191

##### New member
i have an answer already but i just want to double check with you guys

#### MarkFL

##### Super Moderator
Staff member
i have an answer already but i just want to double check with you guys
What I recommend you do is post your answer and all of your reasoning, and then people can tell you if you are correct, and if not, where you may be going astray.

#### Alex919191

##### New member
1 43/144 thats my answer but i dont know how to put it in words

#### mmm4444bot

##### Super Moderator
Staff member
… thats my answer … dont know how to put it in words

Have you decided that you don't need to read or follow the forum's guidelines?

#### Dr.Peterson

##### Elite Member
on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible
1 43/144 thats my answer but i dont know how to put it in words
What question is that the answer to?

I don't think it's asking for a number at all. Rather, if you calculate a probability, and you get something like 1 43/144, which is greater than 1, what must you conclude about your answer?

As a followup, you might then want to look up the rule for probability of "A or B", and think about whether you missed something.

#### pka

##### Elite Member
on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible
I think there maybe a translation problem here. Taking what is posted verbatim, twelve sided dice numbered $$\displaystyle 1\text{ to 12}$$ and product (not sum) of the faces. There are $$\displaystyle 144$$ possible pairs of which we want to count any pair which has a product which is even or has value greater than thirty. Any pair with an even number yields an even product. Thus remove any pair that contains two odd numbers whose product is less than thirty. That count is $$\displaystyle \|(\{1,3,5\}\times\{1,3,5\}\cup\{(1,7)\,(7,1)\,(1,9)\,(9,1)\,(3,7)\,(7,3)\,(1,11)\,(11,1)\}\|=17$$ OR $$\displaystyle 144-17=127$$ pairs the product of which is even or less than thirty. Thus what the is probability of obtaining a product that is an even number or a product of greater than 30 ?

#### Dr.Peterson

##### Elite Member
on any roll of a set of two fair 12 sided dice, the probability of obtaining a product that is an even number or a product of greater than 30, adds to a number larger than 1. Given we know the probability of an event must lie between 0 and 1 explain in your own words if this is possible
The way I read this, it doesn't say "Find the probability ...".

It says, if you do a calculation of the probability by adding some numbers (a common mistake in an "or" probability problem), and the result is greater than 1, what can you say about your answer, and why? It's a true/false question, with explanation.

I suppose I could be wrong; I'm taking the last phrase to mean "explain whether this can be correct", whereas literally it could be taken as "explain (if you are able to)."

#### Alex919191

##### New member
im so confused could someone reply with the answer and say how they did it

#### Dr.Peterson

##### Elite Member
We need to figure out what the problem is really asking. I just stated my interpretation; do you think I am right?

As I read it, the answer is merely: "The answer you got, which is greater than 1, can't be correct, because probabilities can't be greater than 1." I think that's all they want.

Or, as I hinted earlier, you could explain specifically why the method, not just the answer, is wrong: You can't just add two probabilities, because the formula for "or" is

P(A or B) = P(A) + P(B) - P(A and B)​

The two events overlap, so you have to subtract that overlap, which will bring the answer down below 1. That is, in adding, you will have counted even numbers greater than 30 twice.

On the other hand, if you think it is asking for the probability, you can either do what pka showed (which I imagine may be written in a style a bit over your head), or just make a table showing all 144 possible products, mark those which are either even or greater than 30, and count them. You should get the number pka gave (assuming he didn't miss anything). Then put that over 144, and you have the answer.

I dislike questions that are as hard to interpret as this one is; they lead to unnecessary frustration, often over very simple problems.

#### Alex919191

##### New member
i think its asking if it is possible

#### MarkFL

##### Super Moderator
Staff member
I thought, when I initially read the problem, that the student was supposed to determine why we cannot simply add the separate probabilities to get the composite probability, namely because the two events are not independent.

#### Alex919191

##### New member
at the end of the question it asks "explain if this is possible" so it shouldn't be possible because probabilities cant be greater than one

#### Alex919191

##### New member
This is not possible as the formula for probabilities is P(A or B) = P(A) + P(B) - P(A and B) and you can't add separate probabilities because the two events are not independent, probabilities also cannot be above one. is that correct?

#### MarkFL

##### Super Moderator
Staff member
Yes, can you explain why the two events are not independent?

#### Alex919191

##### New member
They aren't independent because one of the probabilities doesn't affect the probability of the other one occurring. or is it the other way around

#### Dr.Peterson

##### Elite Member
Yes, can you explain why the two events are not independent?
I think you mean mutually exclusive, right? This amounts to the second possible answer I suggested.

It's not at all clear how much the student is expected to explain, but this more extended answer can't hurt!

#### Alex919191

##### New member
This is not possible as the formula for probabilities is P(A or B) = P(A) + P(B) - P(A and B) and you can't add separate probabilities because the two events are not independent, probabilities also cannot be above one. is that correct?
so would that be the answer

#### MarkFL

##### Super Moderator
Staff member
I think you mean mutually exclusive, right? This amounts to the second possible answer I suggested.

It's not at all clear how much the student is expected to explain, but this more extended answer can't hurt!
Yes, mutually exclusive is in fact what I meant. Independence is something else entirely...thanks for the correction!