Final answer:
The reliability of a product with two independent components, each having a failure probability of 0.10, is calculated as the product of their individual reliabilities (0.90 each), which results in a total reliability of 0.81 or 81%.
Step-by-step explanation:
To calculate the reliability of a product composed of two independent components where each has a failure probability of 0.10, we must consider that reliability is the probability that both components will function correctly.
Since the components are independent, we can calculate the reliability by multiplying the probability of each component not failing. The probability that a single component does not fail is 1 minus the failure probability, so for each component, it is 1 - 0.10 = 0.90.
The reliability of the product is then the product of the individual reliabilities:
Reliability = (Reliability of Component 1) × (Reliability of Component 2)
Reliability = 0.90 × 0.90 = 0.81
Therefore, the reliability of the product is 0.81 or 81%.