 And welcome back. Today what we're going to do is talk about the probability of dependent events. Okay so in a previous video we watched about independent events and this one we're going to talk about dependent events. Okay so now what do we mean by dependent events? Okay these are events that actually depend on one another. Okay either one of them depends on the other event happening. You have to meet certain criteria or something to that effects. Okay so for example actually we'll go through this notation first then we'll get to the example. Okay so if A and B are those two events and they are dependent events then the probability of both of them happening event A and event B happening is equal to the probability of the first one happening times the probability of the second one happening assuming that the first one has already happened. Okay that's also red down here where this notation here is the probability of B given that A has occurred. So you can think of this vertical line here as kind of like a this has occurred so after this this event has occurred after this little bar here this event has occurred. Okay so that's one way you can look at it. Alright so this is an example of a dependent event. A red and blue number cube are rolled. Okay red and blue so we can keep track of which one is which. Find the probability of red rolling a six and the sum is greater than nine. Explain why the events are dependent. Okay well actually the events are dependent because of this word right here. Okay so this event is dependent is dependent because okay now this word sum means I need to add two things together. Okay so when I add two things together well I need two things I need one of them to roll a number and I need the second one to roll another number. So what I need is I need two numbers one from one cube and one from the other and so what I'm what I what this means is I am dependent because I need both cubes to roll a number to make a sum. Okay so this vent is dependent because sums need two numbers to add together. Okay now that's that's just a very basic way of of going over why this would be a dependent event. Okay so we've explained why it's dependent so now change a little colors here now we're going to actually get into the probability. Find the probability of red rolling a six and and the sum is greater than nine so I'm gonna say that the sum is greater than nine. Okay so now when we work with this I'm gonna kind of refer back up to here if we're looking at dependent events what we look at is if we want both of these events to happen this is going to be equal to the probability of the first event happening times the probability of the second one happening given that the first one has already happened. Okay so this is what the notation is going to look like equals the probability of the first one happening so red six all right times the probability of the second happening us getting a sum greater than nine assuming given that we already have a red six. Okay so what is the probability of getting a red six so I roll the red cube what's the probability of getting a six that's pretty easy it's going to happen one out of every six times. Okay that's pretty easy probability to come up with this first part is usually not really that difficult to come up with the probability. Okay the second part on the other hand assume that you have rolled a six. Okay so what I'm gonna do is I've rolled a red six already using my little colors here I've already rolled a red six already and now for the blue number so to change my colors here I can either roll a one a two a three a four a five or a six. Okay I got a lot of choices of the numbers that I could roll. So in this case what we want is we want a sum greater than nine well a sum greater than nine would be a 10, 11 or 12. Okay those are the three numbers that I'm looking for a 10, 11 or 12. Okay so now looking at my choices that I have I can roll a six and a four a six and a five or a six and a six. Okay any one of those combinations will give me a sum that is greater than nine assuming that I have already rolled a six again given that I have already rolled a red six. So what this tells me is that there's six four six five six six there are three such events that meet my criteria of a sum greater than nine out of a total of well one two three four five six I have a total of six six one six two six three six four six five six six there are six such events that could happen okay now sometimes you might have to do a small diagram like this write out these numbers so you can figure out your totals. Okay multiply these together this would be three out of 36 which is a total reduces down to one 12th and there we are. So one out of every 12 tosses of the two number cubes is going to give me a red six and a sum greater than nine there we go. And that's an example of our dependent events okay again remember dependent means that they depend on one another either they both depend on one another or I guess the examples that we'll have is that only one of them depends on the other this red six didn't really depend on the other cube okay the sum greater than nine that definitely dependent on both cubes because I need both numbers to get that sum okay anyway that is the probability of dependent events thank you so much for watching and we'll see you next time