Odds of getting 1 decent prize out of X chances, Y decent prizes, and Z total prizes.

#1
I am invited to play a game where there are 10 good prizes, 300 losers prizes, and I have 5 tokens to spend playing, 1 per turn.

I know the odds on my first pull are:

10/300 = 3.33%

Second pull (provided I do not get a good prize on the first pull) are:

10/299 = 3.3445%

And so on...

Now, let's vary the mix:

What are the chances, before I do my first pull, that in using my ten tokens I will get at least one good prize, and how do I express said formula?

And, to make it really tricky, can this be done in Excel?
 

Dason

Ambassador to the humans
#2
Re: Odds of getting 1 decent prize out of X chances, Y decent prizes, and Z total pri

Can you tell me the probability that you get 0 good prizes in 1 turn? In 2 turns?
 
#3
Re: Odds of getting 1 decent prize out of X chances, Y decent prizes, and Z total pri

Well...

I have 10 chances. I have 10 good prizes. I have 290 bad prizes. My odds of getting a good prize in 1 turn is 3.333% Ergo, I am pretty sure my odds of NOT getting a good prize are 96.666%

As for my odds of getting at least 1 good prize in 2 attempts, that is pretty much my question.

Let me rephrase it...

I have a bag with 10 green marbles, and 290 red marbles. If I reach in and pull out 10 marbles at random, what are the odds I will pull out at least 1 green marble?
 

Dason

Ambassador to the humans
#4
Re: Odds of getting 1 decent prize out of X chances, Y decent prizes, and Z total pri

Yes I understand. I was trying to guide you along since "the probability of getting NO good prizes" is easier to calculate than "the probability of getting at least one good prize" but if you can get the first one then getting the second one is very easy as well.