Statistics

Probability

To solve this problem, we need to calculate the number of defective video games that are expected to be delivered after testing, given the defect rate and the accuracy of the test. We will follow these steps: 1. Calculate the number of defective video games produced. 2. Calculate the number of defective video games that are correctly identified by the test. 3. Calculate the number of defective video games that are not identified by the test (false negatives). 4. Calculate the number of non-defective video games that are incorrectly identified as defective by the test (false positives). 5. Determine the total number of defective video games delivered, which is the sum of false negatives and the number of non-defective games that are incorrectly not delivered due to the test's inaccuracy. Let's go through these steps one by one. ### Step 1: Calculate the number of defective video games produced. Given a defect rate of 0.95%, and 100,000 video games manufactured: $$ \text{Number of defective games} = \text{Total number of games} \times \text{Defect rate} $$ $$ \text{Number of defective games} = 100,000 \times 0.0095 $$ $$ \text{Number of defective games} = 950 $$ ### Step 2: Calculate the number of defective video games that are correctly identified by the test. Given the test is 98% accurate at determining if a video game is defective: $$ \text{True positives} = \text{Number of defective games} \times \text{Test accuracy} $$ $$ \text{True positives} = 950 \times 0.98 $$ $$ \text{True positives} = 931 $$ ### Step 3: Calculate the number of defective video games that are not identified by the test (false negatives). False negatives are the defective games that the test fails to identify: $$ \text{False negatives} = \text{Number of defective games} - \text{True positives} $$ $$ \text{False negatives} = 950 - 931 $$ $$ \text{False negatives} = 19 $$ ### Step 4: Calculate the number of non-defective video games that are incorrectly identified as defective by the test (false positives). First, we need to find the number of non-defective games: $$ \text{Number of non-defective games} = \text{Total number of games} - \text{Number of defective games} $$ $$ \text{Number of non-defective games} = 100,000 - 950 $$ $$ \text{Number of non-defective games} = 99,050 $$ Now, we calculate the false positives: $$ \text{False positives} = \text{Number of non-defective games} \times (1 - \text{Test accuracy}) $$ $$ \text{False positives} = 99,050 \times (1 - 0.98) $$ $$ \text{False positives} = 99,050 \times 0.02 $$ $$ \text{False positives} = 1981 $$ ### Step 5: Determine the total number of defective video games delivered. The total number of defective video games delivered is the sum of false negatives since false positives do not contribute to defective games being delivered: $$ \text{Total defective games delivered} = \text{False negatives} $$ $$ \text{Total defective games delivered} = 19 $$ Therefore, approximately 19 defective video games are expected to be delivered, which means the correct answer is: - 20

Math

A company manufactures video games with a current defect rate of 0.95%. To make sure as few defective video games are delivered as possible, they are all tested before delivery. The test is 98% accurate at determining if a video game is defective. If 100,000 products are manufactured and delivered in a month, approximately how many defective products are expected to be delivered? - 20 - 50 - 950 - 2,000

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