# Calculating chances of winning

new post here on mathoverflow.

I have a question about calculating chance.

My parents got this scratch ticket calendar from one of my sisters. It has 31 scratch off things, one for each day of this month.

There are 9 possible symbols. I don't remember all of them but lets just call them 1 to 9.

if you get 11 time 9 you win 100.000, if you get 10 time 8 you win 5000. So obviously you don't have an equal chance of getting a 9 compared to an 8. But for the sake of simplicity lets say we have equal chances for each symbol.

The chance of getting the symbol you want is 1/9 = 11.1%.

So today is the 9th december. So far we got 5 times number 8. So we are half way there to win 5000.

With the chance of getting number 8 the next square being 11.1% again, what exactly is the chance of getting 5 time number 8 in the coming 22 days?

And how much I like to just get the answer, I would even like it better if someone can explain me how to calculate this so I can check for the other wins aswell :)

If I asked this in the wrong place im sorry.
Let me know and ill delete the question :)
I hope I gave enough information. If I forgot something feel free to ask :) Thanks in advance.

I would just use a binomial calculator. You are running 22 trials, with an (assumed) independent chance of success of $\frac{1}{9}$ for each trial. And you want the probability of greater than 4 successes. Five or more.
I believe your chances are around $8.9\%$.