I am reading the book Database Systems the Complete Book 2nd Edition. A slightly modified Question 13.4.5 states:
Suppose we use three disks as a mirrored group; i.e., all three hold identical data. If the yearly probability of failure for one disk is F, and it takes H hours to restore a disk, what is the yearly probability data loss?
My answer is $(F*(F*H/365*24)^2)*6$
I would like to know if I am right. I will explain the reasoning behind my answer:
In order for data loss to occur, all 3 disks must fail within a time period of H hours.
The probability that the first disk fails is $F$. The probability that the second and third disks fail within $H$ hours of the first disk failing is $(F*H/365*24)^2$.
Thus the probability of all disks failing within a time period of H hours is $F*((F*H/365*24)^2)*6$.
The reason we multiply by 6 is because there are 6 ways in which this event could happen:
123 132 213 231 312 321
I have trouble with probability when dealing with events that can occur in multiple ways. So the only part of the reasoning that I am unsure about is the part where I multiply by 6. Are all 3 disks failing one event, or are they 6 different events?