WEBVTT
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all right, We're given to events A and B
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, and we're also given that the probability of these
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greater than zero And what we want to prove is
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that the probability of a given B plus the probability
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of a not given B equals one. And for
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that, we're just gonna use based there, in
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which are mathematical representation. Probability of egg oven be
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which looks like this. All right. So far
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, so good, we're gonna actually represent ah,
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the probability of a not given be using based armas
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. Well, so we'll just sub in some may
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not send for the A's there. Do the same
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on the denominator. And keep in mind that the
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compliment of a knot is just a so this just
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becomes a probability of a and probability of be given
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a All right now since these two have the same
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denominator, adding them is rather simple will end up
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with this. We'll just add the numerator tze and
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throw the common denominator on the bottom. So,
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Streit this Outworld quick all over. All right.
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And if we step back and look this fraction,
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we realize, Hey, the numerator and denominator,
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they're the same. So this equals one. Thus
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be proven that since the fractions add up to one
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their probability, the vein given B plus the probability
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of a not given B equals one mission makes sense
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. Even given a condition, something is either true
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or not true. So there you go.