WEBVTT
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Okay, So in this problem we are discussing the
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reviews for a certain scientific journal. Um, we
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consider and the reviews could be classified as short,
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medium or long. And they could be written with
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word. Or they may be written with latex,
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which would be specified as w prime. So 60%
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of the papers are short, 30% are medium one
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or a 10% are long. And then of the
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short papers, 80% are written in word of the
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medium papers, 50% of Britain inward. And of
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the long papers, 30% are written in work.
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The first problem we want Thio solve is we want
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to find out what the probability that a particular that
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any review was submitted inward so we can find that
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out Using the love total probability. So pfw is
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equal to p of W given s times p of
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s and I'll give the justification. So each of
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these options the S M and L are exclusive.
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A paper can't be short and medium and they were
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exhaustive. If it's not short, medium or long
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, then it's not possible. So we can apply
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total love Total probability. So you have p of
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w given s time two p of s plus the
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p of w given em times the probability of em
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plus the probability of W given l Times the probability
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of l which we can plug in our values.
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We have 0.8 times 0.6 plus zero, five times
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0.3 plus 0.3 times 0.1 That comes out to 0.66
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then. So that's for a from B. I
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want to answer If a selected review was submitted inward
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, what are the posterior possibility? Probability is rather
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of it being short, medium or long. So
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what that means is we want to find a p
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. M s Given w p of n Given W
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and p of l given W. P. M
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s given w can figure this out using Bayes theorem
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. That would be p of W given s times
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p of s divided by p of w give w
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we figured out before, So that would be 0.8
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times 0.6 0.6, divided by 0.66 That comes out
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to 0.73 p. F. M. Given value
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is similar deal here just with a M and seven
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s. So that is 0.5 times 0.3, divided
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by 0.66 which gives US 0.23 and p. M
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L Given W is 0.3 times 0.1, divided by
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0.66 gives US 0.4