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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.

A factory produces three types of products: A, B, and C. 60% of the products are type A, 30% are type B, and 10% are type C. The quality control for these products is as follows:
- For type A products, the probability of being defective is 5%.
- For type B products, the probability of being defective is 3%.
- For type C products, the probability of being defective is 7%.

The probability that a randomly chosen product is defective is:

Learn how to calculate the overall probability that a randomly selected product from a factory is defective. This involves using the Law of Total Probability, considering defect rates for three product types (A, B, C) and their respective proportions. Suitable for high school students in Grades 10-12.

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