With a binomial distribution we can calculate the probability of winning x times in k trials. But, what if the number of trials is increased by each time you "win".
Say for example, you have 100.00 dollars, each scratch off costs 5 dollars. Each scratch off you win 20% of the time and you win 10 dollars.
What is the probability that you will get to play at least 30 times?
Well we can calculate the number of times we'd need to win in order to be able to play 30 times. We'd need 10 more tickets at 5 dollar per ticket so we'd need to therefore win 50 dollar --> we need to win 5 times.
But, i don't think the answer is as simple as calculating the binomial distribution for: 5 wins in 30 trials...
Background: This isn't homework... i'm trying to calculate the odds of winning a prize in an online game.