WEBVTT
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all right, were given some statistics about light aircraft
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that disappear over a certain country. So we're given
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that 70% of said aircraft are discovered. So let's
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make a probability tree. Just d'oh, Help us
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visualize this a little bit better. In fact,
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I'm gonna take a little longer. We know that
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70% of them are discovered or 0.7. We know
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that they're 4 30% are not discovered. In addition
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, we know that 60% of the point aircraft that
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are discovered having emergency locator. So we're just gonna
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say loc for locator that 60% here, therefore without
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a locator 0.40 here. You know, I just
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speaking to say I'm gonna throw zeros at the end
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of everything. In addition, 90% of the aircraft
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not discovered do not have a locator. So no
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locator 90% which means there's 10% of those that do
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have a locator. Now, in order to find
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the tail end of these branches of this probability tree
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, which is gonna multiply as we go down the
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line, for example, for this spot here,
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she's gonna be a 70% chance of being discovered and
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then, given that it is, discover a 60%
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chance of this locator 600.7 times 0.6 is point for
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two, and we'll go down the line. So
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point 7/10 0.0.4 to 8. 3 10.1 Uh,
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0.10 0.3 times 0.9. All right, look,
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let's look at the problem for a As for the
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probability that airplane is not discovered given that has an
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emergency locator using our definition of conditional probability, we
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know this is the probability not having not being discovered
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. Intersection having a locator all over the probability of
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having a locator. All right, the probability of
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not being discovered with a locator we can just see
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here it's 0.3 The probability of having a locator.
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Well, that's just gonna be the probability of having
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a locator and being discovered. What's the probability of
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having a locator and not being discussed? It's gonna
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be point for two plus 20.3 which is gonna be
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0.45 if you divide this out. Not is 0.67
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As for part B, we're on the probability that
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plane will be discovered given that it does not have
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a locator. All right. Same general set up
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. We want to find the probability that it's discovered
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. Intersection No locator over a probability I'm not having
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a locator. So the probability of being discovered?
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No locator 0.28 The probability of not having a locator
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is just gonna be one minus the probability of having
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a locator. So that's gonna be one minus 10.45
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just 0.55 If you divide this out, this is
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0.509 and there you go.