Probability of Compound Events

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“Right here we go in this video. We re gonna talk about finding the probability probability of compound events. So we are going to be measuring the chance of two more events happening so for example. What is the probability of the spinner landing on yellow and the dye landing on three now since this probability is not going to be based on any previous results.

I know that i m going to be finding the theoretical probability. So the number of ways. The event can occur to the total possible outcomes now a way that i can represent my total possible outcomes is to draw out a sample space. Okay a sample space.

Usually you ll see a sample space as a table or a tree diagram and you may also see a sample space is just a list okay for this example. I m going to create a i ll create a table okay so what i m gonna do is i can i m just gonna represent the entire possible outcomes that can happen when i roll or when i spin the spinner and when i roll the die so let s see what can all happen i can spin a the spinner in it land on red and i can roll a 1..

I could spin the spinner. It lands on red and i can roll a 2 a red and a 3. I could spin. I read and roll a 4 red and roll a 5 like it s been a read and roll of six okay so as you can see i could do this for each color.

I could spin a blue and land on one blue and two blue and three blue in for booting five. And so forth. So i m just going to continue this process until i represent all of the possible outcomes up and i skipped a number there should be four all right and we got red blue green and yellow. Now this could also be considered a list if you want to i didn t really create a table like i said.

I was gonna do but anyway you get the point. I have all of my total possibilities when i spin this spinner and when i roll this die..

Represented right here in in my sample space. Okay. So now i can easily look at my sample space. And write the ratio of the number of ways.

The event can occur. So the spinner landing on yellow and the die rolling on three that can happen one way to the total possible outcomes. And i see it that i have one two three four five six there s four rows of six possible outcomes. So that means.

I have 24 total possible outcomes. So 124th so this would be the probability of this spinner landing on yellow and the dye landing on three alright now we can also solve this using another method..

Okay. We are also we can also multiply the probability of each event. Okay. So the first event was the spinner landing on yellow and i see that there s one yellow took four total possible outcomes.

So this would be one fourth times the probability of this diet landing on three there s one three out of six total sides okay. So it s one over six. Okay don t put three over six. Just because we re looking for the diet to land on three there s only one three on this number cube.

So that s why we have to have a one here not a three all right so we multiply this out we re going to multiply fractions straight across 1 times. 1 is 1 4 times..

6 is 24 and as you can see we get the same answer. So those are two ways of finding the probability of compound events. Creating a sample space and multiplying the probability of each event alright and there you go probability of compound events. Thanks for watching.

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