Chapter 6.2, Problem 29E

A manufacturer guarantees a product for 1 year. The time to failure of the product after it is sold is given by the probability density function

     $f\left(t\right)=\{\begin{array}{cc}.01e^{-.01t}& ift\ge 0\\ 0& \text{otherwise}\end{array}$

Where t is time in months. What is the probability that a buyer chosen at random will have a product failure

1. (A)  During the warranty period?
2. (B)  During the second year after purchase?