today we're doing part one of two video lessons on experimental and theoretical probability let's get to it all right we're going to start with experimental probability and just like the name suggests experimental probability is just a probability based on the results of an experiment to find an experimental probability it's pretty simple the probability of an event is just the number of times that event occurs divided by the total number of Trials pretty simple all right now that we understand that let's get to our first example all right example one the table shows the results of spinning this spinner 50 times what is the experimental probability of spinning a blue okay well first where did I get those results uh I actually didn't make a spinner and sit here and spin it 50 times there's a great website nctm the link is in the description you can customize your own spinner uh you can decide how many sectors or sections the spinner has you can choose the number of spins in this case I did 50 and maybe the best feature is that you don't have to sit there and wait until all 50 happen you can click skip to the end and then it'll just show your results so if you want to do this on your own go to the website and give it a try all right so now for the question the event is spinning a blue so the probability of blue we'll put that in parentheses is going to be equal to the number of times it landed on Blue which if we look at the table was eight divided by the total number of Trials well how many times did we spin the spinner if you remember we spun it 50 times you could even double check by finding the sum of all of those counts and if you add them up the answer is 50. so the probability of blue is going to be 8 over 50 but we can simplify that divide the numerator and denominator by 2 and that gives us 4 over 25 that would be the fraction uh answer we could change that into a percent right pretty easy times numerator denominator by 4 to get it over a hundred which would be 16 or even as a decimal we could write it as 0 0.16 which means out of all 50 of those spins 16 of the time it landed on blue let's try another example example two I caught blank out of blank pencil flips if this trend continues how many pencil flips should I expect to catch out of 50. hmm well that's a very good question notice this question is not really finished it says blank and blank pencil flip so I guess to find an experimental probability first thing I need to do is an experiment all right let's collect some data so I'm going to flip it 10 times see how many I catch out of 10. oh that oh good good good [Music] all right not my best performance maybe I'm a little bit Rusty but at least we've got some results so I caught seven out of the ten pencil flips now we can use those results to find my experimental probability for catching a pencil flip so probability of a catch well that's equal to how many times did I catch it seven out of how many times did we do the experiment how many times did I actually flip it total well I did it 10 times so experimental probability of catching a pencil flip is seven out of 10. now we need to use that to help me predict how many catches I would get out of 50. I don't want to sit here and do 50 pencil flips and count all of them I want to use the information from doing the 10 to make it hopefully a good prediction so a couple different ways we could do this if I think about it that experimental probability means I caught seven tenths of the flips right seven tenths or seventy percent or 0.7 I caught seventy percent of them or seven tenths of the flips so if I'm doing 50 flips I can figure out how many I should expect to catch by just using multiplication if you think of it this way seven tenths of the flips well seven tenths of 50 in this case that just means 7 10 times 50. so if I do that again before I multiply I always always try to simplify first so I can simplify the 10 and the 50 that becomes one that becomes five seven times five is thirty five so out of 50 flips I would expect to Catch 35 of them now here's a few to try on your own all right so that was experimental probability stay tuned for the next video to learn all about theoretical probability