I'm not quite sure how to tackle this question,
The number of customers arriving to a bank and a supermarket each independently follow a Poisson process with intensity 3 and 5 customers per hour, respectively. What is the probability that the first customer will be to the bank ?
Any help/guidance is appreciated
hint
The time $T_B$ for a customer to arrive at the bank is exponential with mean $1/3$ and the time $T_S$ for one to arrive at the supermarket is an exponential with mean $1/5$, independent from $T_B.$ You just need to compute $P(T_B< T_S).$