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The lifetime \(L\) (in years) of a washing machine follows an exponential distribution with parameter \(\lambda\). A family buys a new machine. On average, this specific model lasts for 10 years before breaking down.
Determine the parameter \(\lambda\) of the exponential distribution.
What is the probability that the machine functions for at least 15 years?
Six years later, the machine is still working. What is the probability that it functions for 4 more years?
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