Experimental vs Theoretical Probability

in this video i'm going to talk about two different types of probability we have experimental versus theoretical probability when think about theoretical probability this is probably the one that you're most familiar with think about if say what's the probability for flipping heads on normal two-sided coin there's two possibilities heads and tails the probability of you choosing heads would be one out of two theoretical probability is based on the math it's based on the outcomes that you actually can see that are on the coin right now technically have theoretical probability of getting flipping heads one out of two times theoretical probability is what is expected to happen based on the math when i'm thinking about theoretical probability i'm thinking about what's the total number of possibilities or possible outcomes in the situation and then how many of those outcomes would give me the desired event so if i'm finding the probability of heads know that there are two possible sides on coin heads and tails and know that there is just one head so my theoretical probability is one half just like can find the probability of heads that's one half can also find the probability of tails which in this case would be the exact same thing right again still have two options favorable outcomes or tails would be one out of two possibilities this would be theoretical probability here's where it gets tricky and where we start to distinguish the two experimental probability is when you actually start flipping the coin so in theory we should be able to get heads one out of every two flips in theory but you could have really bad luck right you could get tails over and over and over and over and over again it could be long time before you got heads right that would be where we get into experimental probability experimental probability is found by doing an experiment and observing the outcomes we have different equation for how we want to think about this for experimental probability we want to write our fraction as the number of times the event occurs out of the total number of trials let's go back to our flipped coin and look at this through the experimental probability lens let's say that flip normal two-sided coin ten times in row let's say that three of those times get tails and seven times get heads if i'm thinking about what's the probability for getting let's say heads i'm going to think about that flipped the coin 10 times and got it 7 out of 10 times now remember this is what actually happened to me this is not based on the math based on the math had my probability of one half right this is based on what actually happened so the probability of heads out of 10 flips would be that got 7. remember you need to simplify if necessary don't need to in this case when i'm thinking about the probability of tails in my case flipped it three times so that would be three times out of ten trials three tenths would be my experimental probability for flipping tails whenever i'm trying to remember the difference between the two i'd like to think about what hear in real life so you'll hear people say well in theory it should happen that is based on the math right when they say in theory they're not basing that on what's happened to them they're saying that based on the math this should happen right if flip coin twice should get heads however the experimental probability is what actually happens when flip it the denominator is based on the number of trials so your experimental probability is going to look very different almost always than your theoretical probability hope this video was helpful and you now know the difference between experimental versus theoretical probability in theory you should