The Probability Line | Understanding Probability | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover the probability line, which will help us better understand probability. Remember, probability tells us how likely something is to happen. The probability line gives us a visual of the likelihood an event happens. We will go through five probability examples here. We will then place them on the probability line and talk about the likelihood of each event. We are going to use this spinner right here for our probability examples. So, if we spin the spinner, we're going to look at the probability of where it lands. You'll notice there are eight equalsized sections on the spinner. So, each section has an equal chance of being landed on. Now remember we can use the probability formula to find the probability of something. P for probability of an event equals the number of favorable outcomes over the total number of possible outcomes. Let's jump into number one where we have the probability of spinning a 10. For each example here I've already calculated the probability. So here there aren't any tens on the spinner. So we have zero favorable outcomes. There are eight total sections that the spinner can land on. So eight is our total number of possible outcomes. Then our decimal is zero and our percent is 0%. So we have our probability as a fraction decimal and percent. Now, taking a look at this probability, there's no chance we land on a 10. And if we go down to the probability line, which is down here, we can see that it starts at zero and goes up to one. All probabilities will fall somewhere on this line. And then we can see that we have 1/2 in the middle. We can use fractions, decimals, or percents when working with the probability line. So I have all three below. Now, thinking about number one, a probability of zero falls right here. So I'm going to put a star and then I'll put a 10 next to it to label it. When we have a probability of zero, we call that an impossible event. There's no way for it to happen. So, for example, spinning a 10 here is an impossible event. There's no 10 on the spinner. So, we can't spin a 10. Let's move on to number two, where we have the probability of landing on red or blue. So, either of those is a favorable outcome here. Either will work as far as this event happening. There are four red sections and four blue sections on the spinner. 4 + 4 gives us a total of eight favorable outcomes. So, eight favorable outcomes over eight total possible outcomes. So, our fraction is 8 over 8. Our decimal is 1 and our percent is 100%. All eight sections are either red or blue. we have a 100% chance of landing on red or blue. This event is right here on the probability line. Our fraction is one. Remember, whenever we have the same numerator and denominator, that fraction equals 1. And then our decimal is 1 and our percent is 100%. I'll write red or blue here to label this. When we have a probability of one or 100%, we call that a certain event. We are 100% certain it will happen. Next, for number three, we have the probability of landing on an odd number. The odd numbers are 1, 3, 5, and seven. So that's four favorable outcomes. over eight total possible outcomes. So there's a four out of eight chance of landing on an odd number. Now you'll notice I also have 1/2 written right here. That's because 4/8s simplifies to 1/2. Depending on the situation, class, the directions, whatever the case may be, you may need to simplify the fractions. So I did want to include that something to keep in mind. Then we have our decimal 510 and our percent is 50%. This event is right here on the probability line. It's right in the middle and I'll put odd in order to label it. This is what we call an evenchance event or a 5050 event. It's just as likely to happen as it is not to happen. Just like flipping a coin. 50% chance of heads, 50% chance of tails. For this example, we have a 50% chance of landing on an odd number and a 50% chance of landing on an even number. So again, this is an evench chance event. Moving on to number four, we have the probability of landing on a one or a two. So, both are favorable outcomes. Either will work. The spinner has one section with a one and one section with a two. 1 + 1 gives us a total of two favorable outcomes over 8, which is the total number of possible outcomes. There's a 2 out of eight chance of spinning a 1 or a two. Now 2/8s simplifies to 1/4. So I wanted to include that as well. Our decimal here is 25 hundreds and our percent is 25%. Now this event is going to be right around here on the probability line. I'll put our fraction. So 2/8s which simplifies to 1/4 our decimal 25 hundreds and then our percent 25%. So I'll put those underneath and then let's label this one or two. This is what we call an unlikely event. It's more unlikely to happen than it is to happen. Yes, of course, unlikely events happen, but there's less than a 50% chance. There's a higher probability it doesn't happen. And let's think about this. There's two favorable outcomes out of eight total outcomes. One section with a one and one section with a two. So again, two favorable outcomes. And that's up against these six other sections that have other numbers. So think about what has a better chance of happening. Landing on a one or a two or landing on any of the other numbers. So again, this is an unlikely event. An event in between 0 and 1/2 is an unlikely event. Lastly, let's take a look at number five. We have the probability of landing on a number less than 8. So that's 1 2 3 4 5 6 or 7. Those are all of the numbers less than eight on the spinner. That gives us seven favorable outcomes over eight total possible outcomes. So we have a 7 out of eight chance of landing on a number less than 8. Our decimal is 875,000 and our percent is 87.5%. This event is about right here on the probability line. So let's put the fraction decimal and percent. And then we can label this less than Eight. This is what we call a likely event. It's more likely to happen than unlikely to happen. There's a higher probability it happens than doesn't happen. We have more than a 50% chance here. Anything in between 1/2 and 1 is a likely event. And thinking about this specific event here, we have seven favorable outcomes. Seven sections with a number less than eight. And that's up against only one section with a number not less than 8. So this is a likely event. Now, to wrap things up here as an overview of the probability line, the closer an event is to zero, the less likely it is to happen. So, the further left we go, the lower the probability. The closer an event is to one, the more likely it is to happen. So, the further right we go, the higher the probability. So, there you have it. There's an explanation of the probability line which helps our overall understanding of probability. I hope that helped. Thanks so much for watching. Until next time, peace.