A bank has 3 tellers, each occupied with 1 person, average time at each teller is 5 minutes. What is the probability of waiting less than 3 mins? This is an exponential distribution with $\lambda =\frac{1}{5}$
The way this goes is:
The first customer finishes before three minutes OR second customer finishes before three minutes Or third customer finishes before 3 minutes.
With this, it would 
$$3\int_0^3 \lambda e^{-\lambda x}dx =3(1-e^{\frac{-3}{5}})$$
Is this correct?

These are not mutually exclusive, so you don't just add them up.
Instead, the customer is still waiting if:
The first customer is still going at 3 minutes AND the second customer is still going at 3 minutes AND the third customer is still going at 3 minutes.
These are independent.
