Please note: probability is not my strong suit, so you should probably double-check this solution. However, I think it is correct...
To find the probability of five successes, we must first determine the total possible combinations:
The probability of five successes is the sum of the probabilities of each individual combination of five successes:
In fact, we can generalize this:
Conversely, the probability of not winning is simply:
and the probability of not winning 91 times in a row is:
The probability of losing each encore ticket:With encore (keeping it simple) a player has 2, 1 in 10 chances of winning something per play.
The probability of losing eight of these is:
Just multiply the probabilities:What are the odds that nothing will be won from this lot of tickets?
I'll let you compute that.