To solve this problem, we need to calculate the overall probability that a randomly chosen product is defective. The factory produces three types of products: A, B, and C. We are given the following information:

• 60% of the products are type A, 30% are type B, and 10% are type C.
• The probability that a product is defective is 5% for type A, 3% for type B, and 7% for type C.

The overall probability of selecting a defective product can be calculated using the law of total probability:

$P(\text{defective}) = P(\text{defective} | A)P(A) + P(\text{defective} | B)P(B) + P(\text{defective} | C)P(C)$

Substitute the given probabilities:

$P(\text{defective}) = (0.05 \times 0.60) + (0.03 \times 0.30) + (0.07 \times 0.10)$

Let's compute this:The overall probability that a randomly chosen product is defective is 0.046, or 4.6%. This corresponds to option a. 0.046.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. How would the probability change if the percentage of type A products increased to 70%?
2. What is the probability that a product is not defective?
3. How would you compute the probability if there were 4 types of products instead of 3?
4. If the defective rate of type C products decreased to 5%, how would the total defective probability change?
5. How would you interpret the results if all product types had the same defective probability?

Tip: In probability problems, always ensure the sum of the event probabilities is 1 to validate the setup.