I hope someone can help as I'm really struggling with this one and so far my research has left me stumped.
Ok, if a prize draw raffle is held and there is 500 entries for 10 prizes are the odds of winning 1 in 50?
Now if the same draw was held but to start 50 of the 500 entries were drawn to move onto another draw and 10 of those 50 win a prize, would the odds still be 1 in 50?
Assuming no ticket is allowed to win more than one prize, yes and yes. For the first case, there are 10 winning tickets out of 500, so a random ticket has a 10/500 chance to win a prize. For the second, you have a 50/500 chance to be moved, then if you are a 10/50 chance to win, so your overall chance is $\frac{50}{500}\times\frac{10}{50}=\frac{1}{50}$.
Going by the heading, and assuming that by "odds" you mean probability,
P(win for some one left in first draw) $= \dfrac{10}{450}= \dfrac1{45}$,
P(win for someone shifted to second draw) $ = \dfrac{10}{50} = \dfrac15$
The two aren't the same, and neither will the odds in favor,
at $1:44$ and $1:4$, if you actually meant odds.