Greetings citizens of the Junior High. It has recently come to my attention that many of you are slightly confused about two types of probabilities- theoretical and experimental. Well, I'd like to help you figure out the difference between the two.
First up: theoretical probability. This is simply an educated guess at what will happen in a situation. For instance, the theoretical probability that citizens of the Junior High will wash their hands after using the restroom to help prevent the spread of the "stomach flu" is 1 or 1/1 or 100%. It should be a sure thing, especially since there are signs stenciled on the walls that say "Please Flush" and "Please Wash Hands". You can refer to this probability as P(washing hands). Simple hand washing after using the restroom can limit the spread of the "stomach flu", which really isn't a flu at all, but often an e. coli bacterial outbreak.
In essence, a theoretical probability is just a hopeful prediction.
Now, we'll take a look at an experimental probability. This type of probability is a ratio based on the number of favorable outcomes out of the total number of trials. Quite simply, we conduct an experiment and observe what happens. For our example, if we notice that the water ran 5 times for 8 people leaving the restroom we can conclude that the experimental probability is 5/8 = 5 out of 8 = .625 = 62.5% of the people using the restroom washed their hands.
In many cases the theoretical and experimental probabilities are not equal. Often times the experimental probability is greater than the theoretical probability.
Unfortunately, in our example, the best we can hope for is that the experimental probability matches the theoretical probability. Especially since everyone can read the writing on the wall- "Please Wash Hands".
We are not even going into theoretical and experimental probabilities of the "Please Flush" signage.
Citizens of the Junior High, remember: Only you can wash your hands.