Probability The Basics EXPLAINED with Examples

hey guys it's mark from ace tutors if you are struggling with probability this video is for you over the next couple minutes i'm going to be giving you quick background and high level description of probability and then in future videos we're going to dive deep into some of the trickiest and most popular concepts in statistics to help you ace your class so overall probability is an incredibly powerful tool that we use every day with or without knowing it whether you are calculated poker player or professional researcher or even just looking outside to see whether you should bring an umbrella or not we all use probability all the time at its core probability is branch of math that we use to calculate the likelihood of certain events to see how it works let's look at one of the most common and simple examples of probability flipping coin now if were to ask you the probability of flipping tails most of you would intuitively be able to tell me that it's 0.5 or 50 percent but how did you come up with that to see where this comes from let's look at simplified formula for probability to calculate the probability of random event which we can write like this you would find the number of possibilities that satisfy that event or condition and divide it by the total number of possibilities that exist so for our corn example to calculate the probability of getting tails we know that there are two total outcomes possible either heads or tails so that becomes our denominator then we know that there is only one of those possibilities that would satisfy our desired condition of flipping tails so that becomes our numerator and gives us the same result of one-half as before and if we were to do the same thing for calculating the probability of flipping heads we would get the same result of one half now although this was simple example it provides great insight into the rules that all probability follows the first rule says that the probability of any and every event must fall somewhere between zero and one with zero being something impossible like me trying to figure out my girlfriend's thinking and one being something that's absolutely certain like you smashing that like button to help support us making these videos anyway the next rule says that if you were to add up all the probabilities of all the different outcomes of certain event the result will always equal one which makes sense if you perform some action there has to be some outcome for the coin example there are only two possibilities each with probability of one half and if you were to add those up you would see that it does equal one finally the third rule is written like this where this little represents the complement of or the probability of not happening so this says if you take the probability of happening and the probability of not happening it must equal 1. which again makes sense because for any given outcome to an event the outcome either must occur or not occur there's no possibility of middle ground where it does and doesn't occur so that's the basics of probability in future videos i'll be going into much deeper detail on the subject and covering much more complex concepts once again if you enjoyed or found this video helpful please subscribe to our channel to see more of our content thanks again for watching and remember you have big dreams don't let class get in the way