Poisson - Arrival of customers to a booth at exhibition Suppose the number of customers visiting a booth at an exhibition is a Poisson with rate 14 customers per hour. Find the probability that the first customer arrives at the box office within 5 minutes This one should I use pmf or cdf ? If I use pmf, then p(1) = 0.3633

If $N_t$ is the number of customer arriving in the interval $(0,t]$, then $$N_t\sim\text{Poisson}(\lambda t= 14/\text{hr}\cdot t = 14/(60\text{ min})\cdot t).$$

Notice that the phrase "first customer arrives in the first five minutes" means at least one customer in 5 mins. Hence, you are being asked for $$P(N_5 \geq 1) \tag1$$

You can also recall that the time until the first arrival $T$ follows an exponential distribution with mean $1/\lambda$. Hence, you are being asked $$P(T\leq 5)\tag 2$$

Verify that $(1)$ and $(2)$ are equivalent. Hint: Try use the complementary probability instead.