Question

You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T ? t) = e^{-frac{t}{5}}, for all t ? 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T ? 2) = e^{-frac{2}{5}} = 0.6703. I purchase the product and use it for two years without any problems. What is the probability that it breaks down in the third year?

          You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies
P(T ? t) = e^{-frac{t}{5}}, for all t ? 0.
For example, the probability that the product lasts more than (or equal to) 2 years is P(T ? 2) = e^{-frac{2}{5}} = 0.6703. I purchase the product and use it for two years without any problems. What is the probability that it breaks down in the third year?

$You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T ? t) = e^-fract5, for all t ? 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T ? 2) = e^-frac25 = 0.6703. I purchase the product and use it for two years without any problems. What is the probability that it breaks down in the third year?$

Added by Cristian M.

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