Short Answer 
The expected number of defective products is calculated using conditional probability, with a defect rate of 0.95% and an accurate test rate of 98%. By multiplying the defect probability by the total number of products (100,000), it is estimated that approximately 950 products will be defective.
Step 1: Understand Conditional Probability
To find the expected number of defective products, we first use the concept of conditional probability. This involves understanding that the defect rate of the products is 0.95%. Hence, we know that for every 100 products, about 0.95 can be expected to be defective.
Step 2: Calculate Probability of a Positive Test Result
Next, we need to assess how accurate the test is. The test we are using is described as being 98% accurate. This means the likelihood of a positive test result (that the product is deemed defective) is 0.98, and the chance of a negative result is 0.02. We will use this information to find the probability of identifying defective products correctly.
Step 3: Compute the Expected Number of Defective Products
Finally, we calculate the expected number of defective products that will be delivered. This is done by multiplying the probability of a defective product being tested positive by the total number of products. Therefore, the formula is:
- Expected number of defective products = Probability of defect * Total products
- Calculating this gives us 0.0095 (defect rate) * 100,000 (total products) = 950.
Hence, approximately 950 defective products are projected to be delivered.