[citation][nom]Sakkura[/nom]Incorrect. If they are not mutually exclusive, you just have to use a different formula
(A or B) = P (A) + P (B) - P (A and B)this is equivalent toP (A or B) + P (A and B) = P (A) + P (B)So the combined probability of either one of the drives, or both of them, failing, is equal to the sum of the probability of each of them failing individually.[/citation]
I'm aware of the basics of statistics, but that's still not how this works. It works in large sample sizes due to the law of averages (for example, by adding up hours to compare to MTBF and get number of drives failed in a time period), but not on individual drives.
Refer to my example of a drive with five components. 20% failure rate for five components does not equal a 100% failure rate as a whole.
[Edit] Clarifying the math to put this to rest.
Or, think of it this way. If there's a 50% chance of the HDD component failing after a week, and a 50% chance of the SSD component failing after a week, do you really think 100% of drives are going to have failed after a week? Because if you simply add the probabilities together, that's what you get.
Here's how the math actually works.
We've got the same hypothetical drive with two components, 50% failure rate of either component after a week. We want to know the number of drives which have not failed after one week to get the overall probability of failure.
A drive can fail because of either A or B failing. After one week, half of the drives should have failed because of A. Now, we need to know the percentage of drives that fail because of B
given that A has not failed. This is known as conditional probability, and is a totally different formula than the one you listed.
The equation is P(B|A) == P(A and B) / P(A).
The probability of A and B is easy since the events are independent, you just multiply them together. The probability of A is also easy, since we know it. That gives us the probability of B given A == 0.25 / 0.5, or 50%. So, we expect 50% of the drives which did
not fail as a result of A to fail as a result of B.
Since we know that 50% of the drives did not fail because of A, we can multiply that fraction again by 50% to get the number of drives that did not fail as a result of A but failed as a result of B, or 25% of the whole
Now you can add the probabilities together, for 75% of the total drives failed.
Like I said, you can't just add the probabilities of failure together to get an overall probability of failure.