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Today we’re going to begin our discussion of probability. We’ll talk about how the addition (OR) rule, the multiplication (AND) rule, and conditional probabilities help us figure out the likelihood of sequences of events happening - from optimizing your chances of having a great night out with friends to seeing Cole Sprouse at IHop!

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Hi, I'm Adriene Hill and welcome back to Crash Course Statistics. If you've every seen a face in an onion or a grilled cheese or any other inanimate object, you've experienced pareidolia which is a product of our brains that causes us to see the pattern of a face in non-face objects. This happens because our brains are so good at seeing patterns that they sometimes see them when they're not really there, like a face in this bell pepper. And faces aren't the only patterns we see. Our brains recognize patterns everything especially in sequences of events like the kind we're going to be talking about today as we start talking about probability.

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Alright first let's just establish a more specific definition of what probability is, because the way we use the word in everyday life can be different from the way we use it in statistics. Statisticians talk about two types of probability: empirical and theoretical.

Empirical probability is something we observe in actual data, like the ratio of girls in each individual family. It has some uncertainty because, like the samples in experiments, it's just a small amount of the data that's available. Empirical probabilities like sample statistics give us a glimpse at the true theoretical probability, but they won't always be equal to it because of the uncertainty and randomness of any sample.

Theoretical probability, on the other hand, is more an idea or truth out there that we can't directly see. Just like we use samples of data to guess what the true mean or standard deviation of the population is, we can use a sample of data to guess what the true probability of an event is. Say you play a slot machine over and over and over and over and over and over. You'll be able to guess the probability of winning the jackpot by counting the number of times you win and dividing it by the number of times you played. If you play a hundred time a win six times, you can be pretty sure that the probability of getting a jackpot is around six out of a hundred or six percent.

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