Please, Please help!!! Desperate to get this project done...

[Arwyn]

I need help to find the Mean for the theoretical probability of rolling two twelve-sided dice. I already have the experimental data set to do that... I just need the formula, or some way of knowing how to calculate this. I only have the formula for calculating the probability for tossing two coins.... I don't see how I would do this for rolling two twelve sided dice, please help! Again, I need to know how to get the mean for the theoretical probability of rolling two twelve-sided dice.

Thanks,
Sarah

 

[Deleted member 4993]

I need help to find the Mean for the theoretical probability of rolling two twelve-sided dice. I already have the experimental data set to do that... I just need the formula, or some way of knowing how to calculate this. I only have the formula for calculating the probability for tossing two coins.... I don't see how I would do this for rolling two twelve sided dice, please help! Again, I need to know how to get the mean for the theoretical probability of rolling two twelve-sided dice.

Thanks,
Sarah

If rolled two 6 sided dice - how many ways you can do that?

 

[Arwyn]

I guess 4... but I still don't know how to get the mean. I need to do a probability distribution graph for rolling two twelve sided dice (both for theoretical and experimental), but to do that I need the mew... I only know how to get the mew, or mean, from tossing two coins, what is the formula for doing so with rolling 2 twelve sided dice? If I'm looking for Heads (coin) it is: the sum of H(P(h)) and from there I can get my standard deviation.... I'm completely lost with how to do this for the dice...

 

[pka]

Sorry to say, but really there is no neat formula.
With twelve sided dice, there are 144 possible outcomes (ordered pairs).
There is one way to get a sum of two. There are two ways to get a sum of three.
There are eleven ways to get a sum of twelve. etc
You must find the number of ways to get each sum from two to twenty-four.
The nice thing is that it is symmetrical about sum 13.

 

[Arwyn]

Alright, so, if I know that the probability of getting a sum of 13 is 12/144, how do I get the mean for the theoretical probability?... for coins it is 0(1/4)+1(2/4)+2(1/4)=0+2/4+2/4=4/4=1 but for rolling 2 twelve sided dice? Would it be easier to try and find the probability of rolling a set of numbers than the sum? How do I calculate the mean in either case?

 

[pka]

Alright, so, if I know that the probability of getting a sum of 13 is 12/144, how do I get the mean for the theoretical probability?... for coins it is 0(1/4)+1(2/4)+2(1/4)=0+2/4+2/4=4/4=1 but for rolling 2 twelve sided dice? Would it be easier to try and find the probability of rolling a set of numbers than the sum? How do I calculate the mean in either case?

As with any mean: \(\displaystyle \sum\limits_{x = 2}^{24} {x \cdot P(x)} = 2 \cdot \frac{1}{{144}} + 3 \cdot \frac{2}{{144}} + \cdots + 13 \cdot \frac{{12}}{{144}} + \cdots + 24 \cdot \frac{1}{{144}}\)