> if you take a 0.3% chance every day, you'll land it once a year.
"actualllyyy" you've got a 2 in 3 chance of landing it each year.
1-((1-(0.3/100))^365) = 0.66
EDIT: stop upvoting me, he's right. The question isn't "what is the probability of at least one success in a year", but rather "how many trials, on average, does it take to get one success" - and the answer to THAT is in fact 333, from the geometric distribution.
“actualllllyyyyy” he’s saying something different. If you take a 0.3% chance for N days where N is large, you’ll land it 0.003N times, or once every ~333 days.
The chance of landing it within any particular window of K days is a different concept (which you showed how to reason about).
But you've also got a 20% chance of landing it twice and a 7% chance of landing it three times and a 2% chance of landing it four times and so, on average, you'll land it every 333 days.
"actualllyyy" you've got a 2 in 3 chance of landing it each year.
1-((1-(0.3/100))^365) = 0.66
EDIT: stop upvoting me, he's right. The question isn't "what is the probability of at least one success in a year", but rather "how many trials, on average, does it take to get one success" - and the answer to THAT is in fact 333, from the geometric distribution.