WEBVTT
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All right. So we're given some information about a
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friend of ours who likes going between Los Angeles and
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Washington, D. C. We're given three airlines
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. The probability that that friend uses each airline and
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the probability that they're late pulling either out of Washington
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see or into Los Angeles. So we have a
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hint that recommends that we set up a probability tree
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in a certain way. So we're gonna set up
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that probability tree right now. All right. So
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let a one b airline one a to B.
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Airline to et cetera. All right, so the
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probability of a wanted 0.50 probability of a chooser 0.30
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the probability of a 30.20 that's what we're given.
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All right. Now I'm gonna define a new variable
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l zero ah, one and all to And what
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these mean is as follows l zero means that there
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are no late flights on either end. Ah,
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one means there's exactly one late flight Whether that be
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in l. A or Washington D. C.
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One late flight and l two means both flights are
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late. Now we're given the statistics that ah,
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certain either landing or taking office late in each city
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, and we're gonna use that to our advantage.
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So we're gonna make this lake three pronged thing off
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the site of each of our branches. Right?
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First off, we're gonna find L, too.
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So we're going to say probability of L, too
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. Devon, a one were given that they're late
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into dese on airline one, flights are laid into
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D. C. At 30% of the times and
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laid into L. A. A 10% of the
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time. That means the probability of both occurring 0.3
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times 0.1 0.3 Conversely, probability of no late flights
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on a one. It's gonna be one minus the
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probability the flights are late in D. C.
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So is there a 0.7 times one minus probability?
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They're late in Los Angeles. Is there a 0.9
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? This is 0.63 now for l one. I'm
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gonna shoot the multiplication for this because these are only
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three possibilities, which means the last possibility is just
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gonna be one minus that all of the probabilities.
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So the other probabilities out of 2.66 So we're gonna
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do one minus 0.66 which is 0.54 No, that's
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wrong. Is there a 0.34? So now that
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we've done that for a one, let's do it
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for a two. So probability L too given a
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Jew is gonna be were given that they relate 25%
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and 20% of the time. So they're playing to
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five. I'm 0.2, and that's 0.5 Conversely,
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we have the probability of no late flights into a
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two, which is 0.75 times 0.8 0.6. Finally
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, we have l one given a two, there's
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gonna be one minus 0.65 Just add the other two
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together and this is 0.35 Finally, we're going to
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the same for airline three. So l want l
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, too. Given a three, it's gonna be
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40 and 25%. So 0.4 times 0.25 that's 0.1
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. We have a probability of no late flights on
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a three gonna be 0.6 times 0.75 which is 0.45
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And finally we're gonna figure out what l ones probability
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is, So am I. One minus 0.55 0.45
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All right, so from this we know that the
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probability of l one a one a given a 10.34
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probability of l one given a two equals probability of
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35 Sorry. 0.35 I don't know what I just
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said. The probability of l one given a three
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equals 0.45 Now that we know that what we need
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to find our probabilities of the reverse of this so
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a one given l one probability of a two given
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l one probability a three given L one. Before
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that, we need to find probably ability of al
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one in general. And we can use a lot
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of total probabilities for that. So where it's gonna
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be 0.5 times 0.34 plus 0.3 times 0.35 plus point
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to 10.45 So it's right that over here it's gonna
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be 0.5 times 0.45 waas 0.3 times zero point for
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making sure this is right. Okay, This is
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why we check these things Because that isn't right.
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It's supposed to be 35 and 34 huh? Yeah
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. 34 and 350 wow. That wasn't right.
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It all good thing I checked. Otherwise, that
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would been a little embarrassing. 34 35 plus 0.2
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times 0.45 There we go. And if you compute
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this, this comes out to be 0.365 All right
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, let's use some base there. Um, so
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we This is the probability of a one times the
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probability of l one given a one all divided by
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the probability of l one, it's gonna be 0.50
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point 34 Divide by 0.365 This ends up being 0.4657
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around four decimal places. Same thing here. Probability
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of a two times the probability of l one.
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Given a two all over the probability of that one
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. So this is gonna be 0.3 times 0.35 all
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over 0.365 And this ends up being 0.2877 Finally,
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we have a threesome. Probability of a three.
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Have the probability of l one, given a three
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over the probability of al one. So this is
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gonna be, uh, 0.2 times 0.45 all over
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0.365 and this becomes zero point 2466 and there you
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have it.