Question

Assume that there is a 1% rate of disk failure in a year. If all of your data is stored on a hard disk, with a copy stored on a second hard disk,

what is the probability that both drives will dail in a year?

what is the probability you can avoid catastrophe with at least one working drive?

Drive 1 and Drive 2 fail. What would be the probability of losing your data f you had it stored on three hard drives?

Answer 1

answer:

we are given that probability of failure of disc in a yesr =1/100

let A be the event that 1st disc will fail, and B be the event that 2nd disc will fail

probability of both disc will fail will be

P(A B)= P(A)*P(B)=(1/100)*(1/100)= 1/100000=0.0001

to find the probability that you can avoid catastrophe with at least one working drive we need to calculate the probability of at least one disc will not fail

P(at least one will not fail)= 1-P(not both will fail)= 1-P(A B)

=1-0.0001

= 0.9999

Disc 1 and disc 2 will fail, then the probability of lossing data if it is also stored in 3rd disc, To calculate the probability lets assume that the event of faliure 3rd disc is C

P[(C P(A B)]= P[C(A B)]/ P(A B)

=[1/100*1/100*1/100] / [1/100*1/100[

=1/100= 0.01