Math Problem Statement

Twenty-six of the 200 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective?

Solution

To find the probability of selecting a DVR that is not defective, we need to follow these steps:

  1. Total DVRs: 200
  2. Defective DVRs: 26

To get the number of non-defective DVRs, subtract the defective ones from the total number:

Non-defective DVRs=20026=174\text{Non-defective DVRs} = 200 - 26 = 174

The probability of randomly selecting a non-defective DVR is the ratio of non-defective DVRs to the total number of DVRs:

P(not defective)=174200=0.87P(\text{not defective}) = \frac{174}{200} = 0.87

So, the probability of selecting a non-defective DVR is 0.87.

Would you like further explanation or have any additional questions?

Here are some related questions to explore:

  1. How would the probability change if there were 30 defective DVRs instead of 26?
  2. What is the probability of selecting a defective DVR?
  3. How would you express this probability as a percentage?
  4. If 50 more DVRs are added, with 10 being defective, how does that affect the probability?
  5. How can you calculate the odds in favor of selecting a non-defective DVR?

Tip: Always remember that the probability is simply a ratio between the favorable outcomes and the total possible outcomes.

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Math Problem Analysis

Mathematical Concepts

Probability
Ratios

Formulas

P(not defective) = (Non-defective DVRs) / (Total DVRs)

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8