Question

How do I summarize the possible outcomes of a random variable and their associated probabilities?

Answer 1

It depends on the kind of random experiment you are going to conduct.

Explanation:

Tossing two coins is a random experiment. It outcome are -

Head on first coin Head on second coin - HH
Head on first coin Tail on second coin - HT
Tail on first coin Head on second coin - TH
Tail on first coin Tail on second coin - TT

{HH, HT, TH, TT}

It can be applied to a real life situation. Suppose two sales people are sent to accomplish sales. [This again is a random experiment. Its equivalent is tossing two coins.] Their outcome can be summarized as -

1st Sales Man Success 2nd Sales Man Success - SS
1st Sales Man Success 2nd Sales Man Fail - SF
1st Sales Man Fail 2nd Sales Man Success - FS
1st Sales Man Fail 2nd Sales Man Fail - FF

{ SS, SF, FS, FF}

This is how You can summarize the outcomes.

First try with simple experiment then move to advanced experiments.