The time (in hours) to repair the Slurpee Machine at 7-Eleven is an exponentially distributed random variable with expected value 2 hours. What is the conditional probability that a repair takes at least 10 hours given that the repair has already taken 8 hours?

The exponential is given by \frac{1}{\theta}e^{-\frac{x}{\theta}}

But,{\mu}={\theta} and {\lambda}=\frac{1}{\mu}

So, we get {\lambda}e^{-{\lambda}x}

Since the problem asks for P(T>10|T> 8)

What we then need is P(T>2)

\int_{2}^{\infty}\frac{1}{2}e^{\frac{-x}{2}}dx