The best example I've seen is the birthday paradox. How likely is it for 2 people in a N person class to have the same birthday? You can solve this deterministi

The best example I've seen is the birthday paradox. How likely is it for 2 people in a N person class to have the same birthday? You can solve this deterministically using math pretty easily. But if you modify the question to ask how likely it is for 3 people, or you add things like February 29th and leap years, or you add the fact that births are more likely during summer months, then it becomes extremely difficult to solve this deterministically. Instead, you run a Monte Carlo simulation to get approximate probabilities. This is much simpler to code and can be easily modified to fit new conditions. A Monte Carlo simulation is probabilistic because you use random numbers in the simulation and you won't get a 100% perfect answer but you'll get close enough (and you can do some math to get error bounds).