A genetic experiment on cell division can give rise to at most 2n cells. The probability distribution of the number of cells X recorded is:

$\displaystyle P(X=k)=\frac{\theta^k(1-\theta)}{1-\theta^{2n+1}} $ $\displaystyle for\ 0 \leq k \leq 2n$

where $\displaystyle \theta$ is a constant with $\displaystyle 0<\theta<1$

What are the probabilities that:

1) An odd number of cells is recorded?

2) At most n cells are recorded?