Suppose that $8$ white balls and $2$ black balls will be randomly ordered, from left to right (with all permutations of the $10$ balls equally likely), what is the expected value of the number of balls that will be between the two black balls ?
I gave it a shot and this is where I am stuck.
If $E$ denotes the event that at least one one white ball in between the two black balls, then
$P(E) = 1- P(E^c)$
$P(E) = 1- \frac{(2) (9!)}{10!}$
which gives $P(E)$ to be equal to $0.8$
I am not sure how to define the Indicator function with this information, that would lead me to answer the question.