Suppose two inspectors look at a product and that their probabilities of detecting a defect are 0.98 and 0.97 respectively. Assume that the inspectors detect defects independently from each other. (A) What is the probability that at least one inspector detect a defect? (B) What is the probability that exactly one inspectors find defects in the product?
Added by Philip C.
Step 1
Since they work independently, we can multiply their probabilities of not detecting a defect: P(neither detects defect) = (1 - 0.98) * (1 - 0.97) = 0.02 * 0.03 = 0.0006 Now, we can find the probability that at least one inspector detects a defect by subtracting Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 87 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors. The first inspector detects 90$\%$ of all defectives that are present, and the second inspector does likewise. At least one inspector fails to detect a defect on 20$\%$ of all defective components. What is the probability that the following occur? (a) A defective component will be detected only by the first inspector? By exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
Probability
Independence
2-148. An inspector working for a manufacturing company has a 98% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that 1% of the items its line produces are nonconforming. (a) What is the probability that an item selected for inspection is classified as defective? (b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?
Madhur L.
An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 0.9% of nonconforming items. (a) What is the probability that an item selected for inspection is classified as defective? (b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?
Sheryl E.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD