The probability of selecting a defective digital video recorder (DVR) from the inventory is given by the ratio of defective DVRs to the total number of DVRs.

There are 7 defective DVRs out of a total of 50 DVRs. The probability $P$ is calculated as:

$P = \frac{\text{Number of defective DVRs}}{\text{Total number of DVRs}} = \frac{7}{50}$

Thus, the probability is:

$P = 0.14$

Therefore, the probability that a randomly selected DVR is defective is 0.14 or 14%.

Would you like more details on this? Here are some related questions:

1. What is the probability of selecting a non-defective DVR?
2. How would the probability change if the total number of DVRs increased?
3. What is the probability of selecting two defective DVRs in a row (without replacement)?
4. How does probability relate to odds in this context?
5. What if the defective rate changed to 10 out of 50? How would that affect the probability?

Tip: Always remember that probability is a value between 0 and 1, where 0 means an impossible event, and 1 means a certain event!