Step 1 :Given that there are 100 digital video recorders (DVRs) in an inventory, out of which 29 are known to be defective.
Step 2 :Let's denote the number of defective DVRs as \(d\), the total number of DVRs as \(t\), and the number of non-defective DVRs as \(n\).
Step 3 :So, \(d = 29\), \(t = 100\), and \(n = t - d = 100 - 29 = 71\).
Step 4 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.
Step 5 :In this case, the event is selecting a DVR that is not defective, and the total number of outcomes is the total number of DVRs in the inventory.
Step 6 :So, the probability \(P\) of selecting a non-defective DVR is \(P = \frac{n}{t} = \frac{71}{100} = 0.71\).
Step 7 :Final Answer: The probability of randomly selecting a DVR that is not defective is \(\boxed{0.71}\).