# how many tickets should i buy in this raffle?

There is a raffle and there are 500 raffle tickets for sale (assume they all get sold)

In the raffle there are 10 prizes to be won.

There is one prize I particulary want to win (I don't bother about the other prizes, athough i would take them if my prize has been taken)

Luckely for me not everybody has his or her eyes on this particular prize, say only 10% of the people has, (say The choice of the prize for the other raffle ticket holders is random to which prize they choose, but anybody given a chance will take any prize)

One by one the raffle tickets are drawn, and the winner makes her choice out of the remaining prizes

If I want to have a change of say 30% to win the prize I particulary want , how much raffle tickets should i buy?

And how many tickets if I want to have a change of 25% or 40% to win the prize I want?

This is a combination of your probability of winning and the chance that the item you want is still available.

Takeing them in reverse order, if you win on the $i$th draw ($i\le10$) the probability that the prize is still available is:

$$P_i=\frac{11-i}{10}$$

The probability that the $i$th draw is the first one you win is:

$$W_i=\frac{n}{501-i}\prod_{j=0}^{i-1}\frac{500-n}{500-j}$$

So the probability that you get the prize you are after is:

\begin{align} A&=\sum_{i=1}^{10} W_iP_i\\ &=\sum_{i=1}^{10}\frac{n}{501-i}\prod_{j=0}^{i-1}\frac{500-n}{500-j}\frac{11-i}{10} \end{align}

Expand this, substitute the chance you want and solve for n.