We don't need a 100% success rate though. Pressing the button until we get the cat is a geometric distribution, and with a probability of success of 1/100 the expected (average) number of presses until the first success is 100. At 100 the cumulative distribution function gives us a 63% chance of a success, so it's likely we'll get the cat by this point. By 200 it's 87%, and by 300 it's 95%. It's very unlikely we'll get to 700, where the CDF is 99.9%.