1. 1 in 100 Chance?

I was browsing the forums of World of Warcraft, and it was mentioned in a thread there that the drop rate of something was 1 in 100. Someone was asking, why is it that, after 100 times going for this item 100 times, I still don't have it? Well, i thought the answer was obvious, that as it's on an Random Number Generator then its a different roll each time, and theres just a higher chance it will roll what you want and the item will drop. However, this other person said,

Quote: "You don't know probability. If you run something 100 times with a 1 in 100 chance, that only equates to a ~63% chance it will drop.".

Can someone please explain to me how this works?

2. Originally Posted by mcaelli
I was browsing the forums of World of Warcraft, and it was mentioned in a thread there that the drop rate of something was 1 in 100. Someone was asking, why is it that, after 100 times going for this item 100 times, I still don't have it? Well, i thought the answer was obvious, that as it's on an Random Number Generator then its a different roll each time, and theres just a higher chance it will roll what you want and the item will drop. However, this other person said,

Quote: "You don't know probability. If you run something 100 times with a 1 in 100 chance, that only equates to a ~63% chance it will drop.".

Can someone please explain to me how this works?
The probability of $1$ or more success in $100$ trials with probability of success $0.01$ is:

$p=1-b(0,100,0.01)=1-(0.99)^100\approx 0.634$

where $b(n,N,p)$ denotes the binomial probability of $n$ successes in $N$ trials with probability of success on a single trial of $p$.

Another way of thinking of this is the probability of one or more success in 100 trials is 1 minus the probability of 100 failures.

CB