What is the difference between theoretical and experimental probability

Theoretical probability is what you can calculate without regard to what will happen in the "real world." For example what is the theoretical probability of drawing a red king from a standard deck of cards (no jokers)? It would be 2/52 or 1/26 [The kings would be the king of diamonds and the king of hearts].  That makes absolutely no reference to what would happen in Vegas if you played this simple game for 10 hours.

Before I leave this part of the discussion, there is a computer simulation that mimics this game. It is called the Monte Carlo method. What you do is run a million draws from a computer deck of cards (1 to 52) and draw 1 card. If it is either the King of hearts or the king of diamonds you give yourself 1 point and record that a draw has taken place. If not you just record that a draw has taken place. 

I just ran this simulation and out of a million draws, 38575/1000000 came back as successful. 1/26 = 0.03846 which means that the rounded version was accurate to 3 decimal places. But it was not the same as the theoretical draw.

A real world or experimental probability is like the Monte Carlo method. A survey is another real world or experimental probability. Who would have predicted the results of the last American election? Who would have thought that though Hillary got the popular vote, she was not elected? 

Theoretical: what you calculate.
Experimental: what you get from a sample for example or a survey. Think elections or insurance policies.