Can someone explain Theoretical Probability and Simulations to me?


I’ve been having a hard time with this math chapter. I feel so lost, I try to write notes but i can’t seem to catch up. I’m about to have a test review tomorrow. Do you guys know how to do it or at least think you do?

In: Mathematics

Could you ask more specific questions? This is like “explain economy to me”. Way too broad to explain without knowing what your curriculum focused on and we’d end up explaining a bunch of things you don’t need and missing a bunch of things you do need.

Theoretical probability: before running an experiment, figure out what the odds of something happening *should* be.

Experimental (simulated) probability: do an experiment a bunch, and figure out what the odds of something happening *were*.

Experimental probability should get closer and closer to theoretical probability the more you do it.


* If you roll a 6-sided die, what’s the chance of rolling a 1? Well, the theoretical probability is obviously 1/6. OK, so roll it six times. You don’t roll a 1! Gasp! Shock, horror! Was your theoretical probability wrong? Well, no, you just failed that 1/6 chance six times in a row – sometimes that just happens.
* Roll it six more times, and you get a single 1. Now your experimental probability of rolling a 1 is 1/12. Still not too close to the theoretical 1/6, but closer than the 0/6 it was a moment ago.
* By the time you’re up to 60 rolls, you’re probably getting closer to 10/60. By the time you’re up to 600 rolls, your experimental probability is probably really close to 100/600. By the time you’re up to 6000 rolls, you should be really close to 1000/6000, and if you’re not, then that’s a sign that there’s something wrong with your test (like a badly lopsided die).