Ok, I have a brief homework question and its been a while since I took stats. Can anyone help me with this:

A fortress has two lines of defense. Both are 99.5% secure. How often will it occur that both lines of defense will fail?

 

Fortress A has a 0.5% chance of failure and Fortress B has a 0.5% chance of failure, the chance that both will fail is (0.005*0.005)*100 = .0025%

 

yep

 

Thanks! Thats exactly what I thought!

 

This assumes that the failure of the lines of defense are independent. If not, the probability that both will fail will be higher than .0025%, but you would need to know the conditional probabilities to calculate it.

 

Magician beat me to it, but yes, this assumes independence of both lines of defense.