Extension on a simple probability question

[trap101]

An experiment consists of tossing a pair of dice:

1) Determine the number of sample points in the sample space

2) Find the probability that the sum of the numbers appearing on the dice is equal to 7


Issue: Ok so I know how to do this problem, but my question comes with respect to the second portion. In this specific problem I am able to count the different sample points that make the dice add up to 7 i.e: 6/36 is the answer, but what if this was a larger problem? e.g: Say that instead of 2 dice I had 7 dice and I needed to find the probability of the seven dice adding up to 15...What technique would I have to use to find/count all those sample points? It surely can't be by counting each one individually?

 

[RoshanBBQ]

There are always many different techniques to solve probability problems. For example, I could define a discrete random variable S as the sum of 7 i.i.d. uniform random variables X~U[1,6]. Then, I could compute the probability mass function of S with 7 discrete convolutions, with the answer being F_S(15) where F_S is the pmf of S.

You can also use counting methods (combinations, permutations, etc.).

 

[trap101]

There are always many different techniques to solve probability problems. For example, I could define a discrete random variable S as the sum of 7 i.i.d. uniform random variables X~U[1,6]. Then, I could compute the probability mass function of S with 7 discrete convolutions, with the answer being F_S(15) where F_S is the pmf of S.

You can also use counting methods (combinations, permutations, etc.).

Ahhh. You see I haven't reached that part of my text yet. I looked through it but haven't done any of the work involving those concepts, but now I see what your getting at. Thanks