Valid discrete probability distribution examples

Anthony denoon is analyzing his basketball statistics the following table shows a probability model for the result from his next two free-throws and so it has various outcomes of those two free-throws and then the corresponding probability missing both free-throws 0.2 making exactly one free-throw 0.5 and making both free-throws 0.1 is this a valid probability model pause this video and see if you can make a conclusion there so let's talk about what makes a valid probability model 1 the sum of the probabilities of all the scenarios need to add up to 100% so we would definitely want to check that and also they would all have to be positive values or I guess I should say they can none of them can be negative values you could have a scenario that has a 0% probability and so all of these look like positive probabilities so we meet that second test that all the probabilities are non-negative but do they add up to 100% so if I had point two to 0.5 that is 0.7 plus 0.1 they add up to 0.8 or they add up to 80% so this is not a valid probability model in order for it to be valid they with all all the various scenarios need to add up exactly to 100% in this case we only add up to 80% if this if we added up to 1.1 or 110% then we would also have a problem but we can just write no let's do another example so here we are told you are a space alien you visit Planet Earth and abduct 97 chickens 47 cows and 77 humans then you randomly select one earth creature from your sample to experiment on each creature has an equal probability of getting selected create a probability model to show how likely you are to select each type of earth creature input your answers as fractions or as decimals around to the nearest hundred so in the last example we wanted to see where the probability model was was valid was legitimate here we want to construct a legitimate probability model well how would we do that well the estimated probability of getting a chicken is going to be the fraction that you're sampling from that is our chickens because any one of the animals are equally likely to be selected 97 of the 97 plus 47 plus 77 animals are chickens and so what is this going to be this is going to be 97 over 97 47 and 77 you add them up three sevens is 21 and then let's see 2 plus 9 is 11 plus 4 is 15 plus 7 is 22 so 221 so 97 of the 221 animals or chickens and so I'll just write 97 to 20 ones they say that we can answer as fraction so I'm just going to go that way what about cows well forty-seven of the 221 are cows so there's a forty seven to twenty first probability of getting a cow and then last but not least you have 77 of the 221 our human is this a legitimate probability distribution we'll add these up if you add these three fractions up the denominator is going to be 221 and we already know that 97 plus 47 plus 77 is 221 so it definitely adds up to one and none of these are negative so this is a legitimate probability distribution