WEBVTT
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all right. For the first part of the problem
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, we want to figure out what the probability of
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a small cup is and what the probability of decaf
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is. I'll use the letters that I have up
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table soapy of p of S and P of B
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. The probability of the getting a small is just
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going to be the some of the two row elements
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for a small. So we have 14% less 20%
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which is going to give us a total of 34%
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. Or we can write that as 0.34 and similarly
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, the probability of decaf, which is going to
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be 20% plus 10% plus 10% it's going to be
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40% or 0.4 for be. We've learned that some
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if we know somebody that are excuse me. If
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we know that somebody has purchased a small cop,
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we want Thio. Then determine what the probability is
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that they have purchased a decaf and we want to
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interpret this probability so we'll start with the interpretation first
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. So we know we know small than we want
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probability decaf. So we can interpret that as meaning
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we want to find the probability of decaf given small
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. We know that event. The event where they
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have purchased a small coffee occurred. We want to
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know if it also occurred that they purchased a decaf
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. So the probability of D given s is the
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probability of the intersection s divided by the probability of
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s So the probability of D intersection s you could
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just read directly off from the table here. Uh
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, the intersection of D. N s is 20%
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. So we have 0.2 divided by the probability of
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getting a small is 34 or 0.34 This comes out
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to about 0.588 Or we can approximate that to 0.59
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Uh huh. Mhm for C. I want to
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go in the other direction. We know decaf.
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We want probability small so we can interpret that as
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the opposite of this p of s given D,
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which is again the probability of the Intersect s on
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top divided by now. The probability of d you
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know that the probability of the Intersect s as we
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saw it before 0.2 probability of D is 0.4.
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So that gives us that the probability of small given
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decaf is 0.5. We also wants Thio comment on
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how this compares to the corresponding unconditional probability from part
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A. So if we know that somebody's purchased a
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decaf coffee, it is more likely that they have
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gotten a small than in the general case where we
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don't know what kind of coffee they've gotten.