Welcome to lesson 1 of module 1 of an Intuitive Introduction to Probability. So, we're going to talk about probabilities. Before we get into formulas, and calculations it's really worthwhile to think about what is a probability. And how do we define probability? Interestingly, there's not just one definition of probability. There are three widely accepted definitions of probability. And so, before we look at some slides and examples let's talk about the 3 definitions. The first definition: called a classical probability or also is a definition of exact probability is objective probability. It's the one that we use when we play games with cards, or with dice or if you go to the casino. Here, we see I've four options if I choose the card, we see they're 3 black cards then there's the Ace of Hearts. And now if I asked you what's the question if I shuffle those cards and pull a card. What's the probability this is the Ace of Hearts? I think you and I can agree on it it's 1 and a (INAUDIBLE) and then 4 25% probability. Objective, I think there is very little discussion unless you think I'm cheating. There's very little discussion and we can quickly agree on the probability. This particular definition is very limited, It's very simple, intuitive, maybe that's what you saw in high school, in college, or another classes. And we like it because it's so easy but, frankly, in everyday decision making it's utterly useless. The reason is it's very limited it requires that all outcomes, like in these cards all 4 cards are equally likely and we can easily agree on the probabilities. Often that's not the case. And therefore we need 2 more definitions of probability which both actually turn out to be way more useful in everyday decision making. So, let's talk about the second definition. It's called the empirical definition of probability or also the definition according to relative frequencies. What's that? In those situations we look at parsed data. For example, before pharmaceutical company can bring a new drug to market it has to do a lot of tests. The idea behind these tests is now to access the probability that this new drug will help a patient with a particular condition you also want access the probability that where will be side effects So, what does a pharmaceutical company do? It gives the drug in some test to patients and then, it checks out do the patients feel better, do we have side effects? And based on this data it then determines probabilities, empirical frequencies that it has seen in the past in the trials to access the probability of side effects. Similarly, when we look at stock market data, parsed data to say something about the future performance of a particular investment. Then, we also essentially talk about the relative frequency definition. We look at parsed data and from those parsed data points we derive assessments for the probabilities. That's the second definition. Again the empirical probability definition or relative frequency definition. But even that definition is not always helpful. What do you do when there is no parsed data? When you're in utterly new situation? For example, when Apple came out with the iPad they didn't have parsed data on iPad sales. This was also brand new product that hadn't existed before. So, the company couldn't look at parsed data. And it wasn't just a "1 in 4 chance" because it was unclear what could happen in the market. At this point they needed the third definition. The subjective probability definition. The company had to access the likelihood of success, the likelihood of failure, and based on that make the decision on whether to bring the product to market or not. And that's the third definition that's occasion we have to use. Based on, perhaps, my gut feeling, or my life experience I access uncertain situation without data and without the easy counting that I can do with cards. To summarize, the key takeaways of this first lesson there are 3 very different definitions of probability. 1. The first one, the easiest one the exact definition that we use when we play cards. Second, if we have lots of data available and we think this parsed data is relevant for probabilistic assessment we use a relative frequency definition. And finally, the third definition if I don't even have data it's a subjective probability definition. In the next lesson we will define these 3 concepts more precisely using some mathematical language. Thank you and please come back to the next class.