What is Experimental Probability? | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover what experimental probability is. Now, remember, probability tells us how likely something is to happen. In other words, the chance of something happening. Experimental probability tells us how likely something is to happen based on the results of an experiment. It's based on data collected from repeated trials. This will make more sense as we go through our examples. Let's jump into our examples. Starting with number one where we have what's the experimental probability of flipping heads. Now, you'll notice down below we have the results of an experiment that we're going to use to calculate the experimental probability. So, for our experiment here, we flipped a coin. We have two possible outcomes when we flip a coin, heads or tails. So those are our outcomes. Then we have a tally column right here where data was collected as the coin was flipped. Each time we flip the coin, that's called a trial. So after each trial, a tally was made. And then our last column to the right here is the frequency column where everything was counted up at the end. So we had 13 heads and seven tails. That gives us 20 total trials. 13 + 7. So 20 total flips. So we're going to use this information for our experimental probability. Our formula for experimental probability is right here. We have P for probability and then in parenthesis 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 times the event occurred over the total number of trials. So for number one we have the probability of flipping heads that's our event equals and now we need the number of times the event occurred over the total number of trials. So as far as the number of times the event occurred heads was flipped 13 times. So we have 13 over and now we need the total number of trials the total number of flips that's 20 and that's our experimental probability as a fraction 13 over 20. Let's write this as a decimal and a percent as well. Remember to go from a fraction to a decimal we divide the numerator by the denominator. So 13 / 20 here that gives us 0.65 65 hundredths. And now we need our percent. To go from a decimal to a percent, we multiply by 100. And remember, a quick way to multiply by 100 is move the decimal twice to the right. That gives us 65%. And that's the experimental probability of flipping heads based on this experiment and the results. Now you may be thinking that can't be right. The probability of flipping heads is 1/2. It's a 50% chance. And that is true. But that's what we call the theoretical probability. That's what we expect to happen based on reasoning and math. This is the experimental probability. It's based on the results of the experiment. Let's move on to number two where we have what's the experimental probability of spinning a four. So here are the results of the experiment. The spinner was spun 50 times. So we had 50 trials. So we have all of the possible outcomes here. So spinning a one 2 3 four or five. And all of these outcomes were equally likely to occur. Then we have our tally column and frequency column. So we are looking for the experimental probability of spinning a four. Now we need the number of times the event occurred. Well, the spinner landed on four eight times. So eight over. And now we need the total number of trials, the total number of spins. That's 50. So we end up with the fraction 8 over 50. Now this fraction can be simplified if we would like. Let's do that just to show what that will be as well. 8 and 50 have a common factor of two that we can divide both 8 and 50 by. So 8 / 2 and 50 / 2. 8 / 2 is 4 and 50 / 2 is 25. The only common factor between 4 and 25 is 1. So this is simplified. Now 4 over 25 is our simplified fraction. Now, keep in mind both of these fractions are equivalent and correct. So, if you are instructed to simplify your fractions, this is just something to look out for. Now, we need our decimal and percent. For our decimal, we need to do 8 / 50 or 4 / 25. Either way, we get 0.16 hundreds. Let's write this down below here. So we have 16 hundreds and now we need our percent. So we need to multiply that decimal by 100. That gives us 16%. And that's the experimental probability of spinning of four. Now one last thing I do want to mention here is that as the number of trials increase so the more and more trials the experimental probability should get closer and closer to the theoretical probability the expected probability. Basically the more trials the closer we get to what's expected. This is what we call the law of large numbers. For example, for number one, instead of flipping the coin just 20 times, what if we flipped it 100 times, 1,000 times, or even 10,000 times? As those trials increase, the experimental probability tends to get closer to the theoretical probability. So, there you have it. There's what experimental probability is. Experimental probability is based on the results of an experiment. I hope that helped. Thanks so much for watching. Until next time, peace.