[DB]

If you take a 3% chance of getting an infection twice you have a 5.91% chance of the being infected when done.

You are confusing two different issues.

Each event is 3% regardless of how many consecutive successful chances you took previously BUT if you do the event 100 times you have an overall chance of 95.2% of being infected when you completed the 100 risk events.

[Mr. Bird]

I only took baby stats in college, so I acknowledge I could be wrong. But it seems to me that the fallacy in the cumulative risk equation is that the risk too rapidly approaches 100%. Let's stipulate to the 3% failure rate. I don't understand how, if I use a condom 33 times without failure, that the next condom I use will statistically be guaranteed to fail. It just doesn't work that way, does it?