Chapter 4.3, Problem 21BSC

Redundancy in Computer Hard Drives Assume that there is a 3% rate of disk drive failures in a year (based on data from various sources including lifehacker.com).

a. If all of your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with four decimal places.

b. If copies of all of your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with six decimal places. What is wrong with using the usual round-off rule for probabilities in this case?