Question

If copies of all your computer data are stored on four independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? With four hard disk​ drives, the probability that catastrophe can be avoided is

Answer 1

`P(Atleast\ 1) = 0.9999992`

Explanation:

Given

`p = 3\%` --- rate of hard disk drives failure

`n = 4` --- number of hard disk drives

See comment for complete question

Required

`P(Atleast\ 1)`

First, calculate the probability that the none of the 4 selected is working;

`P(none) = p^4`

`P(none) = (3\%)^4`

`P(none) = (0.03)^4`

Using the complement rule, the probability that at least 1 is working is:

`P(Atleast\ 1) = 1 - P(none)`

This gives:

`P(Atleast\ 1) = 1 - 0.03^4`

`P(Atleast\ 1) = 0.9999992`