 If you watched part one of the probability basics, you would probably know that probability is a ratio between the number of successful outcomes and the number of all outcomes. As you may know, ratio is just a number, so it can be expressed in different ways as a fraction, a decimal or using percentages. For example, what's the probability of getting a yellow ball randomly from a box if there are three yellow and five blue balls in it? We already know that we only need to find the number of successful outcomes, which is three, and divide it by the number of all outcomes, which is three plus five, which equals eight, so the probability is three-eighths. 0.375 is also our probability, or if we use percentages, it's 37.5%. All of it is the same, and probability can be expressed by any one of these numbers. Let's see our next example. What's the probability of not getting a yellow ball randomly from that same box? Well, we can calculate it in the same way we did in the previous task. There are five balls that are not yellow, so this probability is five-eighths, but we can think of another way too. We know that one event will certainly occur. We will either get a yellow ball, or we will get a ball that's not yellow. One or the other is definitely happening. That's why the sum of their probabilities has to be one. As a result, the probability of getting a non-yellow ball is equal to one minus the probability of getting a yellow ball. We can use the same trick every time we have opposite events. Events can be independent or dependent. Let's look at two experiments. There are three balls in a box, yellow, green, and blue. In both experiments, we take out one ball from the box, but in the first one, we put the ball back into the box after revealing it, and in the second experiment, we leave it out of the box. Let's try to construct a sample set for two situations in the second round. In the second round of the first experiment, we will get a sample set, green, yellow, and blue. No matter what ball was taken out in the first round, so the rounds are independent. But in the second experiment, the sample set depends on what ball was taken out in the first round. So if we took out yellow, the set will be blue and green. If we took out blue, we will get yellow and green in the second round, and blue and yellow if we took out green. In this experiment, the second round depends on the result of the first round. If events A and B are independent, then the probability of events A and B is equal to the product of probabilities of event A and event B. So, what is the probability of getting five tails in five flips? Here, we don't need to model a big sample set for all possible outcomes. We know that flips are independent, so we can just multiply the probabilities of tails in each round. Now, try to find the probability of getting at least one ace if we draw a card three times and put it back to a 36 card deck each time. Pause the video and try to use the fact you already know about probability to find an answer. If we put the card back, our rounds are independent. Getting at least one ace is the opposite to not getting any. The probability of not getting an ace in any one of the rounds is eight nights. So, the probability of not getting an ace in all three rounds is eight nights times eight nights times eight nights, which is 512 over 729. As a result, the probability of getting at least one ace is 217 over 729. So, now you know the basics of probability and are able to use them to solve problems. If you liked the video, give it a thumbs up and don't forget to subscribe, comment below if you have any questions. Why not check out our Fuse School app as well? Until next time!