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let's say that I've just won some type of contest at a car dealership and they're going to give me a brand new car and in deciding which car they give me their first going to randomly select the engine type so the engine will come in two different varieties and leave there be a four-cylinder four-cylinder engine or a six-cylinder engine and they're literally just going to flip a fair coin to decide whether I get a four-cylinder engine or a six-cylinder engine then they're going to pick the color and there's four different colors that the car has come in so I'll write color in a neutral color so you could get a red car that's not red let me do that in an actual red color closer to red you could get a red car you could get a blue car blue car you could get a green car could get a green car or you could get a white car or you could get a white car and once again they're going to randomly let's say just pick they're going to have red blue green and white in little slips of paper and a bowl and they're just going to pick one of them out so all of these are equally likely so given this that they're just going to flip a coin to pick the engine and they're also going to that all of these the color is all equally likely I want to think about the probability of getting a six-cylinder white car the probability of getting a six-cylinder white car so I encourage you to pause the video and think about it on your own well one way to think about this is what what are all of the equally likely possible outcomes and then which of those match six-cylinder white car well first we could think about the engine decision we're either going to get a four-cylinder engine so the first decision is the engine you could view it that way you're gonna get a four-cylinder engine or you're going to get a six-cylinder engine now if you've got a four-cylinder engine you're either going to get red blue blue green green or white or white and if you've got a six-cylinder engine once again you're either going to get red blue like you see where this is going that's not blue red blue blue green green or white or white so how many possible outcomes are there well you could just count though you could kind of say the leaves of this tree diagram one two three four five six seven eight possible outcomes and that makes sense you have two possible engines times four possible colors two times four you see that right here one group of four two groups of four so this outcome right here is a four-cylinder blue car and this outcome over here is a six-cylinder green car so there's eight equally possible outcomes and which outcome matches the one that we I guess are hoping for the white six-cylinder car well that's this one right over here it's one of eight equally likely events so we have a one eight probability now this wasn't the only way that we could have drawn the titi diagram we could have thought about color is the first row of this tree so we could have said look we're either going to get a let me do it down here so I have a little more space we're either going to get a red a blue a let's not blue changing colors is the hard part a blue a green man a green make it a green or white car or a white car and then for each of those colors I'm either going to go to four cylinder or six cylinder engine so it's either going to be four or six either going to be four or six either going to be four or six either going to be four or six this would be another way of drawing a tea drive a tea a tree diagram to represent all the outcomes so what is this outcome right over here this is a six-cylinder red car this is a four-cylinder blue car right over here which is the one that we care about a white six-cylinder car that's this outcome right over here once again you see you have eight equally likely outcomes and that happens because you have four possible colors and then for each of those four possible colors you have two different engine types