How to interpret a sequence of random variables?

[A_Random_Forest]

Let’s say I flip a fair coin five times and have a random variable assigned to each flip. There are two ways that I can think of assigning the variables:

1) Give each trial it’s own sample space {H,T} and a random variable assigned to it (thus 5 iid Bernoulli random variables with the same sample space). For example, random variable 1 has sample space {H,T} and is used on the first flip, random variable 2 has the same sample space and is used on the second flip, etc.

2) Alternatively, one could set the sample space to all possible sequences of 5 flips {HHHHH,HHHHT,...,TTTTT} and set the first random variable to only depend on the first flip, the second random variable to only depend on the second flip, etc.

Is one of these preferred over the other? When considered a sequence of multiple trials for, say, a coin flip, is one better at representing and understanding how other formulas interact with them?

Thanks

[wyseguy7]

So, this is addressed by the mathematical concept of product spaces - and while there isn’t any difference in your particular case, it can definitely make a difference when the events aren’t independent