Probability of many dices

[ollien]

Hello. I,m new here and i would like to discuss a task that was given in my lecture in statistics.

I found this one quite tricky for me and if someone could give a hand, that would be much appreciated.
it goes like this: We have a three sided dice ( X = 1,2 or 3) and the computer program has been modified so that it can simulate 300 dice rolls simultaneously. Let S be the sum of the number eye on the 300 dices. We want to find the probability that the sum is in the range [560,590] .i. Explain briefly how we can proceed to find the exact distribution of S, and comment on why this in practice is not a particularly sensible strategy when we want to find the truth mentioned above.

I have a grip on many things within probabilities, but this one 'm really stuck on. Hope someone can help me out and how to proceed this.

Sincerely Oliver

 

[JeffM]

Hi Oliver. Welcome to freemathhelp.

Suppose we changed the problem to four rolls. Now the resulting sum will exceed 3 but not exceed 12. And suppose I ask what is the probability that the sum will be 7, 8, or 9.

Very similar problem. How would you solve it? How many probabilities would you need to calculate?

 

[HallsofIvy]

My standard rant; The word "dices" is a verb meaning to cute into small cubes or to play with dice.

There is no noun "dices". "Dice" itself is the plural of the single word "die".