Consider an urn with $a$ red and $b$ blue balls. Balls are drawn out one-by-one, without replacement and uniformly at random, until the first red ball is drawn. What is the expected total number of balls drawn by this process? (Hint: Consider deriving an appropriate recurrence.)
- $\frac{a+b}{a+1}$
- $\frac{a+b+1}{a}$
- $\frac{a+b}{a}$
- $\frac{a+b+1}{a+1}$
- $a$