رویدادهای تکمیلی و قوانین ساده

سرفصل: بخش ریاضی / سرفصل: احتمالات / درس 2

رویدادهای تکمیلی و قوانین ساده

توضیح مختصر

  • زمان مطالعه 3 دقیقه
  • سطح خیلی سخت

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Complementary Events and Simple Rules

Now we can talk about some of the basic probability rules, including the complement rule. So before we talk about the rules, let’s talk about the notation we’ll be using here. We’re gonna be using letters to represent possible events. So, A could be drawing two hearts.

B could be it snows tomorrow. C could be Finland wins a gold medal. And of course with each one of these it would, we’d have to specify the kind of situation in which we’d wanna know the probability of one of these things to happen. In this abstract notation, we’ll write P(A), as meaning the probability of event A.

So again, if A is probability of drawing two hearts, P(A) will be the probability of drawing two hearts in a certain circumstance. For most events, the probability is between one and zero. For a probability to equal zero, that means the event is absolutely impossible, guaranteed not to happen. For an event to have probability of one, that means the event is absolutely certain, guaranteed to happen.

So events that have probability of zero or probability of one usually aren’t very interesting to talk about because there’s no uncertainty. The interesting events in probability are the ones that are between zero and one. The ones where there’s a relative degree of uncertainty. At this point, we can talk about complements. The complement of A is not A.

So whatever A is, for example, if A is drawing two hearts, then, not A would be drawing anything other than two hearts. If A is, Finland wins a gold medal, not A would simply be, Finland does not win a gold medal. So we can represent this visually this sort of way. Now this whole circle is everything that can happen.

Well, everything that can happen, let’s think about this. What’s the probability that of all the things that could happen, one of them happens. Well, of course that’s one. It’s absolutely certain that everything that could happen, something will happen. So the whole circle has a probability of one and so that means that those two areas must add up to one, the probability of A and the probability of not A must add up to one.

Now, little bit of rearranging we can solve for the probability of not A and write it as one minus the probability of A. Okay. This is a huge formula. This is the complement rule and we’re gonna be using this in a variety of circumstances.

This is a highly strategic rule that we’ll talk about how to use. So right now, this is our first rule of probability. We’ll get to some more. I’ll give you some general overview rules, also. These are approximate rules in probability or means add, and and means multiply. Now if you were to stop learning probability right here and just stick with this, you’d do, you’d do pretty well.

You’d do okay. These rules are not exactly true. We’re gonna be clarifying them in the subsequent videos.

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