Theoretical Probabilities Of Simple Events

theoretical probabilities of simple events so this is going to kind of lay the foundation for probabilities for us and we're gonna move forward into compound events and kind of make this bit more complex but this will be good information from this for us to have at the beginning here so we can move forward in this concept of probabilities so start with this little word problem at school fair you have choice of spinning spinner or spinner you win an mp3 player if the spinner lands on section with star in it which spinner should you choose if you want better chance of winning got spinner spinner so there are probabilities here which one is gonna give us the most likely outcome of us winning this mp3 player well these are different kinds of spinners that obviously they have different number of spaces to land on the sizes are different and they have different number of stars so which one actually gives us the better chance of winning this mp3 player so gave us little extra space here so the first thing we want to do we'll start with spinner right over here and first thing we want to know is what's the total number of spaces we could actually land on we flicked this spinner anything could happen but what are the total number basically of like pipe pieces that we could land on and if you count them all up here we should have eight so that kind of acts as our denominator and helps us figure out our basic probability here now how many have stars not too bad we have three of them with stars here okay well to develop the probabilities our theoretical probability you can write probability three ways you could write it as fraction basically we have three out of eight chance here you could actually write this as decimal too and that helps lot of times when you compare them so three-eighths converts into three hundred and seventy-five thousandths or 0.375 and then you can also write that as percent and remember we can just move the decimal point two places over and make this thirty seven point five percent so when you compare them it's actually easier to do it with decimal and percent so we've done that with spinner let's try spin besa spinner got to count up all these smaller places it doesn't have eight it has more than that if you count up all of these places are kind of tiny cut look closely it actually has double the amount of landing spaces it has 16 and it has five stars that we could land on so you basically have five out of sixteen chance of landing on star here and winning that mp3 player so now we need to compare these we can compare the fractions you could butterfly these and figure out what the the largest is or you can turn it also into decimal so if you take 516 to turn it into decimal remember you just divide the numerator by the denominator I'm not going to do the division right here but if you do it you'll get point three one two five and as decimal and then when you convert that into percent two spaces to the right makes this thirty one point twenty five percent so now we can compare which one gives us the higher percent chance the most the the greatest probability of winning this mp3 player well if you look it's this one right over here this is little bit larger have little bit better chance if we spend spinner of winning the mp3 player so this gives us theoretical probability this is simple event this is just one thing we're doing hitting spinner and and compound event is if we did multiple things this is just one as we go through so theoretical probabilities the probability that an event occurs when all of the outcomes of the experiment are equally likely so make sure you write that down equally likely means that when we hit the spinner we could land on any one of these spaces here doesn't matter we hit the spinner could land on star could land on not star of blue but it's equally likely we could land on any of them so what is the probability that the event can occur the event is what what we want to happen we want it to land on star so there's basically like formula that you can use and it's just like set it up there the event was us landing on the star and if we took the number of ways the advent kind of well how many stars were there in there were three so that was the number of ways that we could land on that and the total number of equally likely outcomes well there were eight of those different spaces we could have landed on so basically set it up as fraction numerator denominator and then you can always write it as decimal and then as percent to figure out the best probability all right let's try this one real quickly this is pretty quick you roll in number cube one time what is the probability that you roll three or four write your answer in simplest form couple things here number cube same thing is die or dice you're never gonna see in word problems they're not gonna use dice they're also not gonna use quarters they'll say flipped like fair sided coin something like that they won't say quarters they won't say dice think it has something to do with gambling and they don't like to have that connotation there but just know that fair sided cube is dice and they wear number cube is dice fair sided coin is quarter and just so you don't get those confused so if you on this one what's the probability that you roll three or four write your answer well let's think about this real quick we need the total number how many different spaces can we land on for one die die has six sides so it's like the total number of sections so if we know that we know that die has six of them and then how many are three or four well we just need three or four here and that's two of them so you simplify to over three you could turn it into decimal percent but essentially we have one-third chance of landing on two three or four I'm sorry when we do when we kind of roll this dice or this number cube so how's the sample space of an event related to the formula well it's related in that the denominator is the same as the total number of outcomes so six the denominator is the same denominator didn't write that very nicely but it is the same as the total number of outcomes which means we roll this dice there's fair chance that it could land on one through six we don't know and that's kind of sets up our denominator last two examples real quick very quick spinner has 11 equal side sections marked 1 through 11 finding the probability lot of questions that are like this this is still simple event would real quick just kind of make kind of very quick it's not gonna be very good but real quick spinner 11 sides is kind of tricky because usually they give you an even sided spinner 9/10 so let's say here's our 11 sided spinner here's our Center right over here and we're to assume that these are even sides you have the same chance of landing into each space one of them is not bigger than the other one so this is our not too awesome but pretty awesome spinner 11 sided thank you very much so what are the chances find the probability to land on an odd you spin once and land on an odd number what's the probability of landing on an odd if we hit the spinner well don't know how many odds are there one is an odd 3 5 7 9 and 11 how many odds are there 1 2 3 4 5 there are six and how many total places could we land all there's 11 because there's 11 spaces so 6 out of 11 the probability is 6 out of 11 chance or 6 11s that we can land an odd number alright so also what's the probability of landing on an even number there's still 11 equal sides so I'm going to put 11 there how many evens did we have well probably 5 because 1 2 3 4 5 so that gives us 5 5 11 chance of landing on an even so it's more probable that will land on an odd here so this is theoretical probabilities of simple event and we'll be assuming moving forward into compound events