An Intro to Finding Probability | Basic Probability | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to go through an introduction to finding probability. So, we're going to go through a couple of basic probability examples here. Now, simply put, probability tells us how likely something is to happen. In other words, the chance of something happening. Not all things in life are sure things. We can't predict everything with 100% certainty. Meaning we may not know what's going to happen. So when we are unsure about the outcome, the result of something, we can use probability to help us understand how likely something is to happen. For example, if we flip a coin, it can be heads or tails. We can't predict with 100% certainty. We don't know for sure. But we can use probability to tell us how likely a certain outcome, a certain result will be. Let's jump into number one where we have a spinner and we need to figure out what's the probability that we spin this spinner once and we land on three. Well, let's break this down and we'll start with the probability formula which is right here. We have P for probability and then in parenthesis we have the word event. And an event is whatever we are finding the probability of. Basically an event can be one or more outcomes that we are interested in and focused on. The probability of an event equals the number of favorable outcomes over the total number of possible outcomes. Favorable outcomes are all of the ways our event can happen. Then the total number of possible outcomes, that's the total number of things that can happen. The total number of possibilities. All of this will start coming together as we go through our examples. Let's start with the number of favorable outcomes we have. How many ways can our event of spinning a three happen? So, we need the number of sections on the spinner with a three. Well, there's one. We have one favorable outcome on that spinner. One way that our event can happen. So, favorable outcomes, one. Next, we have how many total possible outcomes do we have? So, how many total sections can the spinner possibly land on? Well, there's section 1, 2, 3, and four. There are four equal-sized sections that the spinner can land on. So, each section has an equal chance of being landed on. So, again, there are four total possibilities. Now, let's use this information to write out the probability, which we are going to write as a fraction, decimal, and percent. So we have P for probability and now we need our event in parentheses that's landing on a three. So let's put a three equals well we need the number of favorable outcomes 1 over the total number of possible outcomes. Four. That's our fraction 1 over 4 1/4. And that's our probability. We have a one out of four chance of spinning a three. Now let's write that as a decimal and a percent. 1/4th as a decimal is 0 25 hundreds. Remember divide the numerator the top number by the denominator the bottom number to go from a fraction to a decimal. And then as far as the percent, we get that percent by multiplying the decimal by 100, which a quick way to do that is move the decimal twice to the right. So our percent is 25%. And this is the probability that we spin this spinner once and land on three. This describes our chances. This helps us understand how likely it is that we spin a three. We actually have less than a 50% chance here. One section out of four has a three and that's up against three other sections that have other numbers. The probability of spinning a three here is more unlikely than likely. we have a higher probability, a better chance the spinner lands on one of the other numbers. So, we call this an unlikely event. Now, with that being said, can we still land on a three? Absolutely. I'm not saying we can't. We're just thinking about the likelihood that we do. So, this is something to start thinking about what the probability is telling us. Let's move on to number two. Taking a look at number two, we have what's the probability of picking a red marble? So, let's say we have all of these marbles in a bowl and we randomly select one without looking. So, each marble has an equal chance of being selected. What's the probability we pick a red marble? Well, as far as our favorable outcomes, we could pick red marble number one, two, three, four, five, six, or seven. So, there are seven red marbles. That means we have seven favorable outcomes. Seven ways that we can end up picking a red marble. Now, we need the total number of possible outcomes. So the total number of marbles, well we have one green marble, two green marbles and then one blue marble. So seven red marbles plus those other three marbles gives us a total of 10 marbles. So we have the probability and then our event is picking a red marble. So we will put red here equals the number of favorable outcomes that's seven over the number of total possible outcomes that's 10. So we get 7 over 10 7/10 that's our fraction. We have a 7 out of 10 chance of picking red. Now let's write this as a decimal and percent. 7/10 as a decimal is 0.7. So 7/10. Now remember, divide the numerator by the denominator to go from a fraction to a decimal. And then as far as our percent, we multiply that decimal by 100. A quick way to do that is to move the decimal twice to the right. Our percent here is 70%. So this is the probability of picking a red marble. This describes our chances. This helps us understand how likely we are to randomly pick a red marble. So thinking about our chances here, we have more than a 50% chance of picking red. We have seven red marbles out of the 10 up against three marbles out of the 10 that are not red. Our event of picking red is more likely to happen than unlikely. We have a higher probability of picking red, a better chance of picking red than picking another color. We call this a likely event. So, there you have it. There's an introduction to finding probability. I hope that helped. Thanks so much for watching. Until next time, peace.