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# Probability of a compound event

CCSS.Math:

## Video transcript

let's say that you're on some type of a game show and you've been doing quite well and you're now at the round where you get to pick your fantabulous vacation and so there are three possible places that you could go you could go on an island Beach vacation island Island Beach vacation you could go skiing on a ski vacation or you could go camping now those aren't the only possibilities because for each of those vacations there's different amount of time that you could go on them so you could go for one day you could go for two days two days or you could go for three days three is in a different color you could go for three days you could go for three days so the first question I did want to know is well what is the and it's going they're going to randomly pick either you know of a one-day ski vacation or a two-day island vacation but the first question I want to know is what are all of the possible outcomes here what is the sample space what is the space from which we are going to pick your particular vacation package well for the sample space we can construct a grid which you could see that I've essentially been constructing while I wrote down all of the possibilities so let me draw out the sample space with these uneven looking grid lines all right I think you get the picture all right so you could go and I'll just abbreviate it you could go on a one day a one day island a one day island trip this one I this is one day island trip you could go on a two day to day actually let me just write it this way all of these are going to be one day right because on the one day column all of these are going to be two days two days two days and all of these are going to be three days because it's on the three day column and all of the ones in this row are going to be island trips so it's a one day island trip to day island trip three day island trip this second roads all ski trips one day ski trip two-day ski trip three days key trip and then finally everything in this third row there are camping trips one day camping trip two day camping trip three-day camping trip so just like that we have constructed to the sample space right over here you see that there's one two three four five six seven eight nine outcomes and let's say that each of these outcomes are a little piece of paper and they put it in a barrel and they roll it up and for our purposes we can assume that they are all equally likely outcomes so we're going to assume equally likely outcomes so if we do assume equally likely outcomes we can figure out a probability may be you know may you live in someplace that's cold and you're really not in the mood to go skiing in fact you'd like to spend several days away from the snow so let's ask ourselves a question what is the probability what is the probability that you're going to win something at least at least two days on a vacation without snow two days on vacation without without snow you're going to randomly pick one of these nine outcomes what's the probability that it's going to be at least it's going to give you a vacation that gives you at least of a case with two days without snow well let's just think a little bit about it we know the sample space and we know each of the outcomes are equally likely there are nine equally equal outcomes here so let's write that down we got nine equal outcomes now how many of the SAC outcomes satisfy this this event this this this constraint at least two day two days of a vacation I mean two day let me write this two days days without snow whether it falls or touching it or whatever so this is you're essentially avoiding skiing you want at least two days on something other than skiing and we're assuming you're not going to go camping in some type of Alpine you're camping in someplace that's warm well let's think about these outcomes so this one is no snow but it's only one day this is two days without snow so we can circle one this is three days without snow so we can circle that one all of these have snow this is one day without snow so we're not going to do this one this is two days without snow and this is three days without snow and so four of the equally likely outcomes satisfy this constraint so you have a 4/9 probability of getting a be getting a vacation that keeps you away from snow for at least two days hopefully found that fun and useful for the next time that you are on some type of strange game show