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

Answer:

$P(Atleast\ 1) = 0.9999992$

Step-by-step 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:

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

$P(Atleast\ 1) = 0.9999992$