 and welcome back today we're going to talk about the probability of independent events okay now notice the plural form of this so what we're going to be talking about are multiple events that can happen and the probability of them happening if they are independent of one another okay so the first thing we got to talk about is independent now what does it mean what do we mean by independent independent events are events that have no bearing on one another okay so these examples that we have down here they don't really have any bearing of one another so let's just kind of jump to the examples find the probability of rolling a six on one number cube and a three on another number cube that's a perfect example of two events that really have nothing to do with one another rolling a six on one and then really a three on a different cube well it's a totally different cube they don't really have anything to do with one another okay so that's what we mean by independent events okay so if the two events that we're talking about a and b are independent of one another then the probability of them both happening is equal to the probability of the first one happening times the probability of the second one happening so basically I just take their individual probabilities and just multiply them together that's basically it okay so find and so just like this example find the probability of rolling a six on one number cube and a three on another number cube so I'm looking for the probability of rolling a six and rolling a three I want to roll both of those so I'm using this and word okay I know these these events are independent of one another so this is simply just the probability of rolling a six times the probability of rolling a three with the other number cube okay remember we got two number cubes here okay so in this case the probability of rolling a six that's going to happen one out of every six times okay on a number cube I have the numbers one through six so if I want the probability of rolling a six one one result is what I want the six is what I want out of a total of six that could happen okay same thing over here for the three that happens one out of every six times for a total of when I multiply these together one out of 36 that is my probability of rolling a six and a three at the same time with two separate rolls okay so again this and word if I want both of these both of these to occur this and word tells me that yes I want both of them to occur if that's the case the probability is I simply just multiply the individual probabilities together okay if they are independent events that is okay so next example find the probability of tossing heads tails and then heads when tossing a coin so it looks like we're tossing this coin three times okay so what that what that means is when you toss heads tails whatever they don't really have anything to do with one another right if you if you if you toss the heads the first time then that's going to have no bearing on what you toss the second time around okay your tails or or whatever the case is okay so again these are independent of another heads tails heads they don't have anything to do with one another okay so I know that this is going to be an independent event okay so this is the probability of tossing a heads then a tails and then a heads on a coin now notice my notation just keeping it nice and simple okay so that is the probability of tossing heads times the probability of tossing tails times the pros probabilities excuse me of tossing heads okay so now we and we can have multiple events we can have more than one event that's okay as long as they're independent of one another that's all that really matters so the probability of tossing heads on a coin is one out of every two possibility or the probability of tossing tails is one out of two and the probability of tossing heads again is one out of two again we're treating these all of these as independent events there's nothing to do with one another so I just treat them as independent independent independent okay so one half one half and one half okay so multiply that all together you get one out of eight okay so the probability of tossing heads tails heads is simply one out of eight okay all right that is the probability of independent events just a quick couple of simple examples of independent events thank you for watching I hope you enjoyed the video and we'll see you next time