What is Theoretical Probability? | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover what theoretical probability is. Now, remember, probability tells us how likely something is to happen. In other words, the chance of something happening. Theoretical probability tells us how likely something is to happen based on the math. So, basically, what we expect to happen based on the math. We use the number of favorable outcomes and the total number of possible outcomes. Theoretical probability uses thinking, reasoning and again math to find probability rather than doing an actual experiment where we would find the probability of something based on the results of the experiment. This will make a lot more sense as we go through our examples. Let's jump into our examples starting with number one where we have what's the theoretical probability of flipping heads. So we are not actually flipping a coin here. We are determining the probability of flipping heads based on the math based on the number of favorable outcomes and total number of possible outcomes. This is the formula we use for theoretical probability. Right here we have P for probability and then in parentheses we have 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 the event can happen. The total number of possible outcomes, that's the total number of things that can happen. The total number of possibilities. So for number one, we have the probability of flipping heads equals and now we need the number of favorable outcomes. So, how many ways can our event of flipping heads happen? Well, one. One side of the coin has heads. So, we have one over and now we need the total number of possible outcomes. Well, that's two. We have two total possibilities, heads or tails. There are two sides of the coin. and we have an equal chance of landing on either. So again, we have two total possible outcomes. So we have a 1 out of two chance of flipping heads. Our fraction here is 1/2. That's the theoretical probability of flipping heads. That's what we expect to happen. That's the likelihood of flipping heads based on the math based on the number of favorable outcomes and total number of possible outcomes. Now remember we can write this probability as a fraction, decimal and percent. We have our fraction. So let's write this as a decimal and percent as well. To go from a fraction to a decimal, we divide the numerator by the denominator. So 1 / two here that gives us 0.5 5/10. So there's our decimal. Now we need our percent. To go from a decimal to a percent, we multiply the decimal by 100. And a quick way to multiply by 100 is move the decimal twice to the right. So this is going to be 50%. We have a 50% chance of flipping heads. And there's our theoretical probability of flipping heads as a fraction, decimal, and percent. Let's move on to number two where we have what's the theoretical probability of spinning a four. So if we spin this spinner right here once, we have an equal chance of landing on 1 2 3 four or five. Let's find the theoretical probability of landing on a four. So we have the probability of landing on a four equals and now we need the number of favorable outcomes. That's one. There's only one four on the spinner. So one over and now we need the total number of possible outcomes. That's five. There are five sections that we can land on. And this is our probability as a fraction 1/5. We have a 1 out of five chance of landing on a four. Let's write this as a decimal and a percent as well. For the decimal, we do 1 / 5. That gives us 0.2 2/10. And then we can multiply that by 100 for our percent. So let's move the decimal twice to the right. That gives us 20%. So we have a 20% chance of landing on a four. And that's the theoretical probability of landing on a four. That's the likelihood based on the math. So there you have it. There's what theoretical probability is. Theoretical probability tells us how likely something is to happen based on the math. It's what we expect to happen based on the math. I hope that helped. Thanks so much for watching. Until next time, peace.