If the odds of winning are 1:176 million how many randomly generated tickets have to be sold so that the chance of a winning ticket existing becomes 99%. 176 million is clearly not the case, since they are randomly generated.
The chance that one given ticket fails is
(175999999/176000000)
so the chance that N independent tickets all fail is
(175999999/176000000)^N
You ask what N makes this expression equal to 1-.99; that is the value of
log(1-.99)/log(175999999/176000000)
Let me Google that for you
810,509,958 tickets
(In very close agreement with another calculator of known high precision.)
Thank you very much. I would never have figured that out. Also, I had never seen “Let me Google that for you.” Very cool.