The first component to fail

MediumRandom Variables~4m

A system runs two components in parallel and fails the instant either one fails. Their lifetimes are independent exponentials: component A has rate $\lambda_A = 0.5$ per year and component B has rate $\lambda_B = 0.3$ per year. What is the probability the system survives beyond 2 years? Give a decimal to four places.

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System lifetime is the minimum of the two.
Min of independent exponentials adds the rates.

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0.2019 (± 0.001)

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The first component to fail

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