Suppose Sony's new PS6 is expected to last for 50 years before it stops working, and this time follows an exponential distribution.

1. What's the probability that a PS6 unit fails within 5 years?

1. Sony is offering a 5-year warranty program but is concerned that this may be too expensive. Suppose that PS6 is a highly demanded item and only 500 were offered for sale to the California residents A Sony-contracted service center is set up in SFO and is capable of handling 50 servicing orders during a 5-year period. What is the probability that more PS6s will fail than the service center can handle within the 5-year period?