Hello deathfromabove

Welcome to Math Help Forum! Originally Posted by

**deathfromabove** I'm entered in a raffle with my friends and we're trying to find out our chance of winning. We have six tickets and there are 20 total tickets for the three prizes. The first drawing will take place and the winning ticket will be put aside, then the second drawing will take place with the winning ticket put aside and so on. What is our chances of winning one of the prizes?

I'm assuming that the question means: what is the probability that we win at least one prize? In which case, we find the probability that we don't win any prizes, and subtract this from $\displaystyle 1$.

So, when the first ticket is drawn, there are $\displaystyle 14$ losing tickets out of $\displaystyle 20$. The probability that one of these is chosen is $\displaystyle \frac{14}{20}$

If we don't win on this draw, then there are then $\displaystyle 13$ losing tickets out of the $\displaystyle 19$ remaining. So the probability that one of these is chosen is$\displaystyle \frac{13}{19}$

Similarly the probability that the third one chosen also loses is$\displaystyle \frac{12}{18}$

So the probability that we don't win at all is:$\displaystyle \frac{14}{20}\times\frac{13}{19}\times\frac{12}{18 }=\frac{182}{570}$

Therefore the probability that we win at least one prize is$\displaystyle 1-\frac{182}{570}=\frac{488}{570}$

Grandad