11. A lot of five identical batteries is life tested. The probability assignment is assumed to be P(A) =



A

(1/λ)e−x/λdx for any event A⊆ [0,∞), whereλ>0 is a known constant. Thus the probability that a battery fails after time t is given by P(t,∞) =

 ∞

t

(1/λ)e−x/λdx, t ≥ 0.

If the times to failure of the batteries are independent, what is the probability that at least one battery will be operating after t0 hours?