Mutually Exclusive vs Independent Events EXPLAINED in 4 minutes

hey guys it's mark from ace tutors and in this video i'm going to quickly explain concept that many students including myself have struggled with and that's the difference between events being mutually exclusive versus independent so first let's start with events being mutually exclusive basically when two events are mutually exclusive from one another those two events can't occur together in other words there is no intersection between these two events mathematically this would be written as the probability of and equals zero good example of this comes in the form of flipping coin if we were to make one event flipping heads and the other event flipping tails each event has probability of 0.5 and they have no intersection because there's no possible way to flip coin and have it land as both heads and tails therefore these two events are mutually exclusive now that we covered that let's move on to independence when two events are independent of one another the occurrence of one of those events has no effect on the occurrence of the other event for example if we were to look at the probability of it raining tomorrow as well as the probability of you smashing that like button to support us making these videos we intuitively know that your much appreciated button smashing has no effect on the weather there is some probability that you liking this video will coincide with it raining tomorrow but it would only be coincidence so as result these events are independent of each other however unlike being mutually exclusive this idea cannot be nicely visualized with venn diagram instead we need to rely on mathematics to determine independence specifically for independent events the probability of both of those events happening is equal to the probability of the first event times the probability of the second event this is the basis for determining independence you may also see this idea written in slightly different way to see that we need to look at the conditional formula that says the probability of given is the probability of and divided by the probability of and if you need refresher on where this formula comes from take peek at our last video for quick reminder now within our formula we see this probability of and component if and are independent we can substitute in our independence formula to this equation and then cancel out the probability of from the top and bottom to get that the probability of given is simply equal to the probability of and this makes sense if the two events are independent and you are trying to find the probability of occurring under the condition that also occurs well it doesn't matter that occurs since they're independent so it just becomes the probability of occurring and this works the opposite way too the probability of given just becomes the probability of now if you take one thing from this video remember that for mutually exclusive events the probability of and occurring together is zero and for independent events the probability of and occurring together is the probability of times the probability of if you found this video helpful please consider hitting those like and subscribe buttons to help us help more students like you thanks again for watching and remember you have big dreams don't let class get in the way you