[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?

[general_re]

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?

No, it doesn't really work that way - your odds on the 34'th time are still 3% for that event. What the cumulative risk calculation does show is that eventually that 3% risk will catch up with you - eventually, you will lose. Might be the first time out of the gate, or it might be the 100'th, or it might be the 1000'th - but the odds that you will win every single time start getting vanishingly small the more times you try it. You may have only a 1 in 6 chance of shooting yourself if you play Russian Roulette, but if you play a hundred times, I practically guarantee you're going to shoot yourself at least once - and like AIDS, once is all it takes to lose big ;)

[NukeMan]

"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?"

No, it doesn't. It isn't statistically guaranteed to fail, either. It doesn't have to be the *next* one, only *somewhere* in that chain of 33 - an important difference.

[DB]

No it doesn't work that way. Read my post 30 and maybe it will make more sense to you.

The 10th coin toss is still 50%. But the overall chances of not tossing heads 10 times in a row is about 1 out of 1000.

P.S. I only graduated high school, and I took the GED to do that early... I'm an engineer now...

[Tauzero]

"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's not, of course. That's not what the cumulative risk equation says.

Wouldn't you agree the odds of living through 100 rounds of Russian roulette are lower than the odds of living through 1 round? The odds of the 100th round, though, are not affected by the result of the first 99. If they were, then you'd get a different equation for the cumulative risk!