Assume that there is a 5% 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 three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

The probability that during a year, you can avoid catastrophe with at least one working drive is 0.9975

The probability that during a year, you can avoid catastrophe with at least one working drive is 0.999875

Step-by-step explanation:

There is a 5% rate of disk drive failure in a year

So, probability of failure q = 0.05

Since the sum of probabilities = 1

So, probability of success p= 1-0.05

                                            =0.95

Part a : all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive

So, n =2

We are required to find what is the probability that during a year, you can avoid catastrophe with at least one working drive

So, he probability that during a year, you can avoid catastrophe with at least one working drive :

Hence the probability that during a year, you can avoid catastrophe with at least one working drive is 0.9975

Part b :  If copies of all your computer data are stored on three three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

Since there are 3 copies so, n =3

So, the probability that during a year, you can avoid catastrophe with at least one working drive:

Hence the probability that during a year, you can avoid catastrophe with at least one working drive is 0.999875