I am currently studying the Poisson distribution, and I am wondering whether the following calculation is possible:
Let $X$ represent the number of people who visit the airport in 1 hour and let $X$ follow a Poisson distribution with a mean of $10$.
Given that 5 people have visited the airport in the first 30 minutes, what is the probability of an additional 10 or more people visiting in the remaining hour?
The Poisson process is based on independent events with a constant (mean) rate per unit of time and is "memoryless". This means that if the process has mean 10 per hour, it has mean 5 per half hour. So you are really just looking for $P(\geq 10)$ from a Poisson distribution with mean 5.