A critical component on a submarine has an operating lifetime that is exponentially distributed with a mean of 6 months. As soon as a component fails, it is replaced bya new one having statistically identical properties. What is the minimum number ofspare components which the submarine ought to carry if it is leaving for a one yeartour of duty and it is desired that the probability of having an inoperable unit causedby failures exceeding the spare inventory be less than 0.02

Let V represent the critical component

$\displaystyle E(V) = 0.5$ =>$\displaystyle \lambda = 2$

The probability of the first time the component fails is:

$\displaystyle P(V \ fails) = 2e^{-2}$

Kind of stuck here. Any hints/suggestions would be greately appreciated.