Probability of Selecting a Defective Product

A shipment containing three types of products: A, B, and C has been processed. The quality control team found that 15% of product A, 10% of product B, and 5% of product C are defective.

Moreover, 40% of the products in the shipment are type A, 35% are type B, and 25% are type C. If a product is randomly selected from the shipment, what is the probability that it is defective?

Let $D$ be the event that a product is defective, and let $A$, $B$, and $C$ represent the three product types. The total probability of selecting a defective product can be calculated using the Law of Total Probability.

The formula for the probability is given by:

$$P(D) = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C)$$