Question

assume that there is a 4% rate of disk drive failure in a year. a. if all 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? b. if copies of all 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? a. with two hard disk drives, the probability that catastrophe can be avoided is (round to four decimal places as needed.)

Explanation:

Step1: Find failure probability

The probability of a disk - drive failure in a year is $p = 0.04$, so the probability of a disk - drive working is $q=1 - p=1 - 0.04 = 0.96$.

Step2: Calculate probability for two drives

For two independent drives, the probability that both drives fail is $P(\text{both fail})=0.04\times0.04 = 0.0016$.
The probability of avoiding catastrophe (at least one working drive) is $P(\text{at least one working}) = 1 - P(\text{both fail})=1 - 0.0016=0.9984$.

Step3: Calculate probability for three drives

For three independent drives, the probability that all three drives fail is $P(\text{all three fail})=0.04\times0.04\times0.04=0.04^{3}=0.000064$.
The probability of avoiding catastrophe (at least one working drive) is $P(\text{at least one working}) = 1 - P(\text{all three fail})=1 - 0.000064 = 0.999936$.

Answer:

a. $0.9984$
b. $0.9999$