I am trying to calculate the probability that any one of 5 independent events occur - each event has a 5% chance.
I calculated by saying the probability of any of n events is:
p1 = 0.05
pn = (1 - pn-1) * p1 + pn-1
For p5 I calculate 22.6%. I also verified this my writing small program which simulates this and found the results close to 22.6%. Is my calculation correct?
The example is from the first chapter of: The Signal and the noise - showing the risk of CDOs. The book says the probability is 20.4% but my calculation says it should be 22.6%.