 Probability. We probably use this word as often as, oh wait, I already said it. Probably. Most of you would probably know what the probability of getting tails in a coin-flipping experiment is. But what is the definition of probability? Let's analyse what we already know about it. Probability is a measure of a likelihood of an event occurring. The bigger the probability, the more likely it is that the event will occur. The lowest probability is zero, and the highest is one, or 100%. So it should be something that varies between zero and one, and grows when the chance of success grows. To construct probability fairly, we first need to make a sample space, which is a set of all possible outcomes of an experiment. For example, sample space for dice-throwing experiment is 1, 2, 3, 4, 5 and 6. Sample space for coin-flipping experiment is heads or tails. For pulling one card out of a deck, it's... For a result in a roulette round, it's... Sometimes it's not as obvious. For example, try to write a sample space for flipping two coins together. Pause the video and try doing it yourself first. The correct sample set is HH, HT, TH and TT, where H means heads and T is tails. We end up with four different events, because HT and TH are different occurrences. So the probability of getting one heads and one tails is higher than the probability of getting two tails. After we construct a sample space, it's pretty easy to find the probability of an event. We just need to find the ratio between the number of outcomes that satisfy our event and the total number of outcomes. For example, let's find the probability of getting more than nine as a sum of two-roll dice. Our event is a sum that's greater than nine. Outcomes that satisfy our event are 5, 5, 6, 4, 4, 6, 5, 6, 6, 5 and 6, 6. The number of all possible outcomes is 6 times 6, which equals 36. So our probability is 6 over 36, or 1, 6. Another example, what's the probability of getting a card of spades or an ace from a standard 52 card deck if we get one out blindly? How many cards satisfy our event? We have 13 spades cards and 4 aces, so 13 plus 4 is 17. But we counted ace of spades two times, so there are only 16 cards. As a result, our probability is 16 over 52, or 4 thirteenths. And now a task for you. There are three blue, five red and four yellow balls in a hat. Can you find what the probability of getting a yellow ball from the hat with only one try is? Pause the video and try to find the answer. The correct answer is a third or four twelts. There are four yellow balls. The total number of balls is 12, so our probability is four twelts or one third. And finally, what does probability show and how can we use it? You could say that even if an event has a probability of one in a million, it still may occur. But it's so low, why would you even consider it? Okay, you're right. But probability also shows us that if you repeat an experiment many times, the ratio between successful outcomes and all the outcomes become closer to your probability of success. If you repeat the experiment with coloured balls 9,000 times, you will probably get a yellow ball in about 3,000 of them. That's why you definitely win on a roulette table the longer you play. This is called the law of large numbers. Watch the second part of this video to find out what restrictions this approach has and what its consequences are.