Probability | Rolling a Die | Basic Probability | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover how to find probability. We will go through five basic probability examples using a die. Now, remember, probability tells us how likely something is to happen. In other words, the chance of something happening. And we can use the probability formula to find the probability of something. 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 is one outcome, one result or a group of outcomes, a group of results that we are interested in that we are focused on. The probability of an event equals the number of favorable outcomes over the total number of possible outcomes. The number of 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. Let's jump into our examples here where we are going to say that we are rolling a fair six-sided die. And a fair die just means we have an equal chance of rolling any of the sides. We have five events here that we're going to find the probability of. For number one, we have what's the probability of rolling a four. So if we roll the dieice once, what's the probability we roll a four? So the four is facing up. Well, let's write the probability as a fraction, decimal, and percent. Let's start with the favorable outcomes. So, how many ways can this event happen? How many sides have a four? And you'll notice we have all of the possible outcomes right here. Those are all of the sides of a six-sided die laid out. One side has a four, so we have one favorable outcome. Now we need the total number of possible outcomes. The total number of things that can happen. So how many possibilities do we have here? How many sides does the die have? Well, six. Our fraction 1 over six. 1 16th. We have a 1 out of six chance of rolling a four. Now as far as the decimal, we can divide the numerator by the denominator. So the top divided by the bottom to convert this fraction to a decimal that's going to be 0.1 and then we have a repeating six. So this is a repeating decimal. Now we can convert the decimal to a percent by multiplying the decimal by 100. And a quick way to do that is move the decimal twice to the right. So our percent here is 16.6 repeating percent. Now we can leave the percent like that or round. Let's round this to the nearest percent as well which is rounding to the ones place. We have a six in the onees place with a six to the right in the tths. So this rounds to 17%. So this is approximately and I'm using the approximately symbol here because we are rounding 17%. And that's the probability of rolling a four. Let's move on to number two where we have what's the probability of rolling an even number. So if we roll the dieice once, what's the probability we roll an even number? Let's start with the favorable outcomes. So out of these six sides of the die, how many are even numbers? Well, we have two, four, and six. So, three even numbers. So, three is the number of favorable outcomes over the total number of possible outcomes, which is six. So, our fraction here, 3 over 6, 36. there's a three out of six chance of rolling an even number. Now, I do want to mention three sixths can be simplified. So, depending on your situation, your class, the directions, whatever the case may be, you may be asked to simplify. Three and six have a common factor of three that we can divide three and six by. 3 / 3 is 1 and 6 / 3 is 2. So this simplifies to 1/2. So either of those will work. Next we need our decimal and we can go from either of those fractions. We get the same thing either way. We get 0.5 510. Then we can multiply that by 100 to get our percent. Our percent here 50%. And that's our probability of rolling an even number. Moving on to number three, we have what's the probability of rolling a five or six? Both of these are a favorable outcome. Both of these will work. We either want to roll a five or a six. Think of it like this. You need to roll a five or a six to win a game. So, what are your chances of rolling a five or a six? What's the probability? One side of the die has a five and one side of the die has a six. So, that gives us two favorable outcomes here. So, two over the total number of possible outcomes, six. So our fraction here 2 over 6 2 6. Now this fraction can be simplified. We have a common factor of two that we can divide 2 and six by in order to simplify here. 2 / 2 is 1 and 6 / 2 is 3. So this simplifies to 1/3. So either of those fractions here will work. Now let's convert this to a decimal. And our decimal here is going to be 0.3 repeating. So this is another repeating decimal. Let's convert this to a percent. We have 33.3 repeating percent. Or we can round this to the nearest percent, which again is rounding to the ones place. We have a three in the ones place with a three to the right in the tths. So this is approximately this rounds to [Music] 33%. And that's the probability of rolling a five or six. Next, moving on to number four. What's the probability of not rolling a one? So our favorable outcomes here, we want anything but one. So all of the numbers except one. So 2 3 4 5 and 6. That gives us five favorable outcomes. And that's over six, which is the total number of possible outcomes. So five over six here, five sixths. We have a five out of six chance of not rolling a one. So again, we're looking for anything but one here. 2 3 four five or six. Now let's convert this to a decimal. We get 0 8 and then a repeating three. So another repeating decimal and then let's convert this to a percent. We get [Music] 83.3 repeating percent. And let's round this to the nearest percent as well. We have a three in the ones place with a three to the right in the tth. So this is approximately this rounds to 83%. So that's the probability of not rolling a one. And lastly, let's move on to number five where we have what's the probability of rolling a number greater than two. So we have three, four, five and six. That gives us four favorable outcomes here. So we have four favorable outcomes over six. The total number of possible outcomes. So our fraction here 4 over 6 4 6s. We have a 4 out of six chance of rolling a number greater than two. Now this fraction can be simplified. We have a common factor of two that we can divide four and six by in order to simplify. 4 / 2 is 2 and 6 / 2 is 3. This simplifies to 2/3. So either of these fractions will work. Now let's convert this to a decimal. We get 0.6 repeating. And let's convert this to a percent. We get 66.6 repeating percent. Now let's round this to the nearest percent as well. We have a six in the ones place with a six to the right in the tths. So this is approximately this rounds to 67%. And that's our probability of rolling a number greater than two. So there you have it. There's how to find probability. I hope that helped. Thanks so much for watching. Until next time. Peace.