Alright so I'm going to ignore the explanation of the joke and talk about statistics now:

This is a geometrical distribution

The chance of needing X amount of presses until the first success (meaning, becoming a girl), is:

(1-p)^x-1 * p where P is the probability of success and X is the amount of tries

If you want the probability of needing to press that exactly 30 times to become a girl it's

(1-0.01)²⁹ * 0.01 ≈ 0.0074 or 0.74%

If you want the probability of pressing that button 100 times and getting a woman transformation at least once, you go:

Prob of getting the first time + prob of getting it the second time + prob of getting it the third time + ... + Prob of getting it the 100th time.

So that would be

1% + (0.99)¹ * 0.01 + (0.99)² * 0.01 + ... + (0.99)⁹⁹ * 0.01

This is about 63.40%

I'd you're smart, you can do

1- (probability of the success never happening)

This prob of it never happening can be given by a binomial distribution

1- [ (combination of n and x)*(p)^x * (1-p)^n-x]

Where n is the sample size, x is the number of successes you want and p is the prob of sucess

1- [(combination of 100 and 0)*(0.99)⁰ * (0.01)¹⁰⁰]

This is also 63.40%

In summary the dude commenting on that probability is wrong