I have 3 mutually exclusive events, probability of each one happening is $\frac13$. What's the probability none of the events happens 3 times out of 3 tries.
My approach is this : $(\frac23*(1+\frac13+\frac19))^3=0.893$
Simulation shows 0.889, That 0.004 makes me think I'm incorrect.
Note:I'm looking for general formula, these numbers in my real problem aren't equal and even change during process.