مثال هایی از قانون OR

سرفصل: بخش ریاضی / سرفصل: احتمالات / درس 5

مثال هایی از قانون OR

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  • زمان مطالعه 2 دقیقه
  • سطح خیلی سخت

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Examples of the OR Rule

Now, that we’ve talked about the generalized OR rule, we can talk about some examples. First of all, let me just remind you. The generalized OR rule says, the probability of a or b is the probability of A plus the probability B minus the probability of A and B. This is one of the big rules of probability.

Notice also this is different from what you might call the naive OR rule, or the rough and ready OR rule. The fact that OR just means add. This rule refines that a bit. We can add and simply add if the events are mutually exclusive. But for generalize events, we need to use this slightly more complicated rule.

So, let’s talk about applying this in a problem here’s a problem and I strongly suggest that you pause the video and solve this on your own and then I’ll show the solution. Supposing Game M the probability of outcome A is .6, the probability of outcome B is .7, and the probability of A or B is .9. What is the probability of A and B happening at the same time?

So we’re given the probability of A or B and we’re looking for the probability of A and B. But it turns out that the OR rule can still help us. So write down the generalized OR rule and then we’ll just plug in. We know the probability of A or B and we know the individual probabilities of A and B.

So we’ll just plug those in. Now we’ll move the unknown to one side and get it by itself, and then we’ll just simplify. The probability of A and B equals .4. So even though we knew the probability of A or B, we used the formula to find the probability of A and B.

And again, if you know the probability of A, the probability of B, and the probability of A or B, then you can solve the generalized OR rule to find the probability of A and B.

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