# How to calculate how lucky you are in a contest. Probability.

You are on a beach full of rocks looking for treasure. The odds of finding treasure under any rock is 1/273. You have looked under 5000 rocks and found only 2 pieces of treasure. How unlucky were you? What are the odds of looking under 5000 rocks and finding only 2 pieces of treasure (when the odds of looking under 1 rock and finding treasure is 1/273)? I assume you have to add the probability of finding 0, 1 and 2 together?

I found this website https://stattrek.com/online-calculator/binomial.aspx. But the numbers aren’t precise enough for me. I would like to convert the odds to something more manageable. I wanted to be able to say, this is equivalent to getting heads X number times in a row for coin tosses. And with my sample data it just turns into “0.9999999” on that site, so its not useful to me.

I think I need “Cumulative probability: P(X ≥ x)”.

I tried the BINOMDIST function in excel. But `=BINOMDIST(10,10,1/2,TRUE)` came out to `100%`. And that doesn’t make sense to me… getting at most 10 heads in 10 tosses is 100% probable? I must be miss interpreting it, but I dont see how, right now.

If someone could help explain it to me.

Ideally I would also like to know how much outside of the norm my sample set is. In other words, I question the validity of the 1/273 odds and want to know the best way to test it.