Basic Statistics

#1
I am sure this is a basic problem that is easily solvable, however, I have not been in a Statistics class in a little over 31 years and have all but forgotten the basic concepts.

Here is my question:
You have 15 treasure chests. In 9 of those, you will find some money and the other 6 are empty. You get to make as many picks as you can until you get 3 empty chests. What is the probability that you pick 3 straight empty chests to end the "game"?

I think the statistical probability would be relatively low, but just not sure of how to calculate it. If you were to play this "game" a second time, what is the probability of picking 3 empty chests two times in a row?

This recently happened to me and I find it amazing that it actually happened in the game I was playing. Any percentages that anyone could supply would be greatly appreciated!!

Matt
 

Dason

Ambassador to the humans
#3
When you say "What is the probability that you pick 3 straight empty chests to end the game" does that mean that you pick 3 empty chests right away at the start? Or could you pick 1 treasure chest and then get 3 empty? So is the question "what is the probability of the first 3 chests you pick being empty" or is it "what is the probability that you choose 0 or more treasure chests and then choose 3 empty chests to end the game"?
 
#4
Dason,

I'm sorry I wasn't clear. The answer to your question is "what is the probability of the first 3 chests you pick being empty". Basically, you make 3 picks and all 3 chests are empty ending the game with $0.00.

Thanks in advance for your help!