How does the probability of an event differ from the probability of a random variable? For example, consider the event where there are 4 babies born.
BBBB, BBBG, BBGB, BGBB, GBBB, GBBG, GBGB, GGBB,
BGGB, BGBG, BBGG, BGGG, GBGG, GGBG, GGGB, GGGG
P(no of girls born is 2): 6/16
Let X be the random variable
X = no of girls born (takes values from 0 to 4).
P(X = 2) = 6/16
So what is the use of defining a random variable and going through all the process of probability distribution? In essence it is same as 9th grade probability.