WEBVTT
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All right, We're given this identity probability of a
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Intersect be given, See, because probability of a
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given be inter sexy times the probability of be given
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C Now, I'm gonna write out our multiplication rule
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to the site here and read clipping a little bit
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at the top. You'll have to forgive that I'm
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also going to write a different expression of it that
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gave us our definition of conditional probability. All right
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, now we're gonna work with this left side because
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it looks simpler using our definition of conditional probability.
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We can write it out like this. This equals
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the probability of a Intersect be in her sexy,
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all over the probability of C Because intersections associative,
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we can put the parentheses wherever we need them to
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. So we're gonna move them over now, On
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this numerator, we're gonna use our base form of
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our multiplication rule. So this becomes probability of oh
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, boy, a given probability are sorry. A
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given, be intersex. See times the probability a
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b intersect. See all over you. See,
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now I'm gonna rewrite this as the probability of a
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given be intersect. See, times probability Aby intersect
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. See all our probability of c. Wait a
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second. That looks like our definition of conditional probability
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. So we got probability of a given. Be
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intersect, See times probability of be given c.
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Well, what do you know? That's what we're
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trying to prove Q e d