10.8 A critical component of the next space shuttle to Europa (the Jupiter satellite)

has an operating lifetime that is exponentially distributed with mean 1 year (ship time). As soon as a component fails, it is replaced by a new one having statistically identical properties. It is known that the one-way travel to Europa lasts exactly 2 years. What is the smallest number of components that the shuttle should stock if it wishes that probability of having an inoperable unit caused by failures exceeding the spare inventory throughout the time of the voyage to be less than 0.02?