Hello Everyone!

Now I've been thinking about this problem:

Suppose you have 6000 songs on your playlist, each of these songs have an equal probability of being played next (I assume even the song that is currently played).

How many songs are expected to play before the song you're listening to now repeats?

I thought of it in this way:

Let $\displaystyle A$ be the event: Current songs replays itself, and $\displaystyle B$ be the event that a new song plays.

Obiously, $\displaystyle A$ and $\displaystyle B$ are independent therefore $\displaystyle P(B) = 1 - P(A)$.

$\displaystyle P(A) = \frac{1}{6000}$ and $\displaystyle P(B) = \frac{5999}{6000}$.

It follows that $\displaystyle E(X) = P(A) + 5999\times P(B) = \frac{1}{6000}+5999\times \frac{5999}{6000} = 5998$ songs.

Is this approach correct?

Thanks!