Final answer:
The question involves calculating the probability that a component's lifetime exceeds 2 years, which can be found using the exponential distribution formula with the mean lifetime but requires additional specifics to provide a concrete answer.
Step-by-step explanation:
The question asks about the probability that the lifetime of at least one component exceeds 2 years. This type of problem is commonly related to exponential probability distributions, especially when dealing with lifetimes of technological or computer components. If this is an exponential distribution, the probability that the component lasts longer than a certain time can be found using the formula P(X>t) = e^{-t/μ}, where μ is the mean lifetime of the component and t is the time we are interested in (in this case, 2 years).
To calculate this, we would need to know the mean lifetime of the component. If, for example, the mean lifetime is given as 10 years (as in Example 5.9 from the provided information), the calculation would involve plugging in the values into the formula to find the probability that the lifetime exceeds 2 years. Note that the question implies there could be more than one component, so if it was the case of multiple components, we should also consider the probability that none exceed 2 years and subtract this from 1 to find the answer. If the problem context is similar to Example 5.9 or Try It Σ 5.12, the question is best addressed using the mean lifetime and exponential distribution properties.