The lifetimes of 5 identical bulbs are exponentially distributed with parameter (lambda=1.25 cdot 10^{-4}left[h^{-1} ight]). All of

The lifetimes of 5 identical bulbs are exponentially distributed with parameter \(\lambda=1.25 \cdot 10^{-4}\left[h^{-1}\right]\).

All of them are switched on at time \(t=0\) and will fail independently of each other.

(1) What is the probability that at time \(t=8000\) hours a) all 5 bulbs and b) at least 3 bulbs have failed?

(2) What is the probability that at least one bulb survives 12000 hours?