 A good understanding of probability and statistics is essential for any citizen of a free society if they want the society to remain free. And that's because if you don't understand probability and statistics, you'll be easily manipulated by those who do. And this includes people and organizing. Good citizens do not need to understand probability or statistics. So let's talk terms of probability. Remember, definitions are the whole of mathematics, all else is commentary. A random experiment is one whose outcomes are, in practice, unpredictable. For example, we might flip a coin and record whether it lands heads or tails. So we can't predict in advance how the coin will land. It's important to keep in mind that random doesn't mean reasonless. How the coin lands is going to be completely determined by the laws of physics and how the coin was flipped. But in practice we don't have enough information to be able to predict how the coin will land before it actually occurs, and that's why this is a random experiment. Or again, we might deal out five cards from a shuffled deck, and again, while the cards that we get are entirely determined by the order of the cards in the deck, we can't predict in advance what cards will be dealt. And if you think about it, this applies to pretty much anything that people do. The set of all possible outcomes is the sample space. Generally we limit the sample space to reasonable outcomes. If you flip a coin, the coin could land heads, land tails, be seized by an eagle and carried off to Canada, and maybe some other outcomes, but we'd probably limit the sample space to landing heads or landing tails. A set of some of the possible outcomes is called an event. The event occurs on one trial of a random experiment if any of its constituent outcomes is the result of the random experiment. Otherwise the event does not occur. And remember, to occur only one of the outcomes in the event needs to be the result of the random experiment. So for example, in a talk show, one audience member is selected to win a car. Is this a random experiment? If so, what are the possible outcomes and some possible events? Let's provide examples where the events occur or don't occur. So even if the game is rigged so that a specific audience member will win, we don't know who that will be, so we can treat the experiment as random. Now one possible sample space is someone wins a car. But this outcome always happens so the outcomes are no longer unpredictable and our experiment is not random. As we'll see later on, choosing the right sample space is extremely important. Since we're picking an audience member, the sample space could be the audience members. Whatever they are, we might list their names. And we could take any subset of these. For example, one event is the set F of female audience members. And another event might be G, the set of audience members over 50. So remember to occur only one of the outcomes in the event needs to be the result of the random experiment. So let's see what could make these events occur or not occur. So to make both events occur, we want a female audience member who's over 50. So if a female aged 57 won the car, both F and G occur. So what if a female aged 42 won the car? In that case, F occurred, the winner was a female, but G did not. They were not over 50. Now if we don't want F to occur, we need to pick a non-female audience member. So if a male aged 65 won the car, F did not occur, but G did because they were over 50. And for a male aged 47 won the car, F did not occur, and neither did G.