The urn bet

1. So the final distribution is not concentrated around 1/2; is uniform over the possible states.
2. Short check for n=2: each occurs with probability 1/3.
3. After $n$ turns, the number of possible red balls is $1,2,\dots,n+1$, and those $n+1$ states are equiprobable: $\mathbb{P}(R_n=r)=\frac{1}{n+1}$ for $r=1,\dots,n+1$.

Back to problem
Answer: Maria is right.
After $n$ turns, the number of possible red balls is:

$$ 1,2,\dots,n+1 $$

and those $n+1$ states are equiprobable:

$$ \mathbb{P}(R_n=r)=\frac1{n+1}\quad (r=1,\dots,n+1). $$

Short check for $n=2$:

• possible states of red at the end: 1, 2, 3;
• each occurs with probability $1/3$.

So the final distribution is not concentrated around 1/2; is uniform over the possible states.