The Reviews editor for a certain scientific journal decides whether the review f

Question

The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1-2 pages), medium (3-4 pages), or long (5-6 pages). Data on recent reviews indicates that 60% of them are short, 30% are medium, and the other 10% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 70% are in Word, whereas 60% of medium reviews are in Word and 30% of long reviews are in Word. Suppose a recent review is randomly selected. What is the probability that the selected review was submitted in Word format? If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long? (Round your answers to three decimal places.)

Explanation / Answer

a)

Let

S, M, L = short, medium, long
W = word

Hence, by BAyes' Rule,

P(W) = P(S) P(W|S) + P(M) P(W|M) + P(L) P(W|L)

= 0.60*0.70 + 0.30*0.60 + 0.10*0.30

= 0.63 [ANSWER]

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b)

Also,

P(S|W) = P(S) P(W|S)/P(W) = 0.60*0.70/0.63 = 0.666666667 [ANSWER]

************************

P(M|W) = P(M) P(W|M)/P(W) = 0.30*0.60/0.63 = 0.285714286 [ANSWER]

**************************

P(L|W) = P(L) P(W|L) /P(W) = 0.10*0.30/0.63 = 0.047619048 [ANSWER]

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