This problem involves acceptance sampling, where a sample of items is randomly selected from a batch without replacement, and the entire batch is accepted if all selected items are free of defects.

Key information:

• Total number of CDs: 1500
• Number of defective CDs: 70
• Sample size: 4 CDs
• The entire batch is accepted only if all 4 sampled CDs are not defective.

To find the probability that the entire batch will be accepted, we need the probability that none of the 4 selected CDs are defective. The sampling is done without replacement, so this is a hypergeometric probability problem.

Step-by-step solution:

1. Total number of non-defective CDs: $1500 - 70 = 1430$
2. The probability of picking a non-defective CD on the first draw is: $\frac{1430}{1500}$
3. If the first CD is non-defective, the probability of the second CD also being non-defective is: $\frac{1429}{1499}$
4. Similarly, the probability of the third and fourth CDs being non-defective is: $\frac{1428}{1498} \quad \text{and} \quad \frac{1427}{1497}$
5. Therefore, the probability of all 4 CDs being non-defective is the product of these probabilities: $\text{Prob(all non-defective)} = \frac{1430}{1500} \times \frac{1429}{1499} \times \frac{1428}{1498} \times \frac{1427}{1497}$

Now let's calculate this probability:

$\text{Prob(all non-defective)} = \frac{1430}{1500} \times \frac{1429}{1499} \times \frac{1428}{1498} \times \frac{1427}{1497} \approx 0.8257$

Thus, the probability that the entire batch will be accepted is approximately 0.8257 (rounded to four decimal places).

Would you like further clarification on any part of this?

Here are five related questions:

1. How does the probability change if the sample size increases to 5?
2. What is the probability that exactly one of the four selected CDs is defective?
3. How would the result differ if sampling were done with replacement?
4. Can you explain how the hypergeometric distribution relates to this problem?
5. How would you determine the number of defective CDs for which a sample has less than a 1% acceptance probability?

Tip: When dealing with probability questions involving sampling without replacement, consider whether the hypergeometric distribution applies for more precise calculations.